The goal is to isolate the variable to one side.

\(\displaystyle 6x^{2}=216\)

Divide each side by \(\displaystyle 6\):

\(\displaystyle \frac{6x^{2}}{6}=\frac{216}{6 }\)

\(\displaystyle x^{2}= 36\)

Take the square root of each side:

\(\displaystyle \sqrt{x^2}=\sqrt{36}\)

\(\displaystyle x=\pm 6\)

The goal is to isolate the variable to one side.

\(\displaystyle 3x^{^{3}}+4=28\)

Subtract \(\displaystyle 4\) from each side:

\(\displaystyle 3x^{^{3}}+4-4=28-4\)

\(\displaystyle 3x^{^{3}}=24\)

Divide each side by \(\displaystyle 3\):

\(\displaystyle \frac{3x^{^{3}}}{3}=\frac{24}{3}\)

\(\displaystyle x^3=8\)

Take the cube root of each side:

\(\displaystyle \sqrt[3]{x^3}=\sqrt[3]{8}\)

\(\displaystyle x=2\)

The goal is to isolate the variable to one side.

\(\displaystyle x^2+20=45\)

Subtract \(\displaystyle 20\) from each side:

\(\displaystyle x^2+20-20=45-20\)

\(\displaystyle x^2=25\)

Take the square root of each side:

\(\displaystyle \sqrt{x^2}=\sqrt{25}\)

\(\displaystyle x=\pm5\)

Step 1: Subtract \(\displaystyle 5\) from both sides:

\(\displaystyle 2x+5-5=19-5\)

\(\displaystyle 2x+0=14\)

\(\displaystyle 2x=14\)

Step 2: Divide both sides by \(\displaystyle 2\):

\(\displaystyle \frac{2x}{2}= \frac{14}{2}\)

\(\displaystyle x=7\)

To solve two-step equations, first move everything that does not have the variable over to the other side of the equation. In order to move the -3 to the other side of the equation, you must do the opposite operation (addition). Keep in mind you must do the same step on each side of the equation every time you change something.

\(\displaystyle 4x-3=33\)

      \(\displaystyle +3=+3\)

The equation should now look like this:

\(\displaystyle 4x=36\)

Next, isolate the variable by moving it to the other side of the equation. Do this by doing the opposite operation (division):

\(\displaystyle \frac{4x}{4}=\frac{36}{4}=9\)

The result should be the following:

\(\displaystyle x=9\)

To solve two-step equations, first move everything that does not have the variable over to the other side of the equation. In order to move the -2 to the other side of the equation, you must do the opposite operation (addition). Keep in mind you must do the same step on each side of the equation every time you change something.

\(\displaystyle 7x-2=47\)

      \(\displaystyle +2=+2\)

The equation should now look like this:

\(\displaystyle 7x=49\)

Then, isolate the variable by moving the 7 to the other side of the equation. Do this by doing the opposite operation (division).

\(\displaystyle \frac{7x}{7}=\frac{49}{7}=7\)

The result should be the following:

\(\displaystyle x=7\)

To solve two-step equations, first move everything that does not have the variable over to the other side of the equation. In order to move the -38 to the other side of the equation, you must do the opposite operation (addition). Keep in mind you must do the same step on each side of the equation every time you change something.

\(\displaystyle 15x-38=82\)

        \(\displaystyle +38=+38\)

The equation should now look like this:

\(\displaystyle 15x=120\)

Then, isolate the variable by moving the 15 to the other side of the equation. Do this by doing the opposite operation (division).

\(\displaystyle \frac{15x}{15}=\frac{120}{15}=8\)

The result should be as follows:

\(\displaystyle x=8\)

In order to find x, you need to isolate it. If x isn't alone, you haven't finished solving the problem! 

Step 1: subtract 14 from both sides of the equation

\(\displaystyle 2x+14-14=58-14\)

\(\displaystyle 2x=44\)

Step 2: divide both sides of the equation by 2

\(\displaystyle \frac{2x}{2}=\frac{44}{2}\)

\(\displaystyle x=22\)

Step 1: subtract 4 from both sides

\(\displaystyle -5x+4=-21\)

\(\displaystyle -5x+4-4=-21-4=-25\)

Step 2: divide both sides by -5 to isolate x

\(\displaystyle \frac{-5x}{-5}=\frac{-25}{-5}\)

Solve:

\(\displaystyle x=\frac{-25}{-5}=5\)

\(\displaystyle x=5\)

Remember, a negative integer divided by another negative integer will have a positive answer. 

Using the foil method we have the following

First: \(\displaystyle x\cdot x=x^2\)

Inner: \(\displaystyle x\cdot3=3x\)

Outer: \(\displaystyle x\cdot-3=-3x\)

Last: \(\displaystyle 3\cdot-3=-9\)

When that is simplified we are left with \(\displaystyle x^2-9\)