Solve (2x-3)(2x+3)-135=0

$$( 2 x - 3 ) ( 2 x + 3 ) - 135 = 0$$

Solve for x

$$x=-6$$

$$x=6$$

Steps Using Difference of Squares

Consider \left(2x-3\right)\left(2x+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$\left(2x\right)^{2}-9-135=0$$

Expand \left(2x\right)^{2}.

$$2^{2}x^{2}-9-135=0$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-9-135=0$$

Subtract 135 from -9 to get -144.

$$4x^{2}-144=0$$

Divide both sides by 4.

$$x^{2}-36=0$$

Consider x^{2}-36. Rewrite x^{2}-36 as x^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-6\right)\left(x+6\right)=0$$

To find equation solutions, solve x-6=0 and x+6=0.

$$x=6 x=-6$$

Steps by Finding Square Root

Consider \left(2x-3\right)\left(2x+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$\left(2x\right)^{2}-9-135=0$$

Expand \left(2x\right)^{2}.

$$2^{2}x^{2}-9-135=0$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-9-135=0$$

Subtract 135 from -9 to get -144.

$$4x^{2}-144=0$$

Add 144 to both sides. Anything plus zero gives itself.

$$4x^{2}=144$$

Divide both sides by 4.

$$x^{2}=\frac{144}{4}$$

Divide 144 by 4 to get 36.

$$x^{2}=36$$

Take the square root of both sides of the equation.

$$x=6 x=-6$$

Steps Using the Quadratic Formula

Consider \left(2x-3\right)\left(2x+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$\left(2x\right)^{2}-9-135=0$$

Expand \left(2x\right)^{2}.

$$2^{2}x^{2}-9-135=0$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-9-135=0$$

Subtract 135 from -9 to get -144.

$$4x^{2}-144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-144\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-144\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-144\right)}}{2\times 4}$$

Multiply -16 times -144.

$$x=\frac{0±\sqrt{2304}}{2\times 4}$$

Take the square root of 2304.

$$x=\frac{0±48}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±48}{8}$$

Now solve the equation x=\frac{0±48}{8} when ± is plus. Divide 48 by 8.

$$x=6$$

Now solve the equation x=\frac{0±48}{8} when ± is minus. Divide -48 by 8.

$$x=-6$$

The equation is now solved.

$$x=6 x=-6$$