(2x-3)(2x+3)=7

Solution for (2x-3)(2x+3)=7 equation:

Simplifying
(2x + -3)(2x + 3) = 7

Reorder the terms:
(-3 + 2x)(2x + 3) = 7

Reorder the terms:
(-3 + 2x)(3 + 2x) = 7

Multiply (-3 + 2x) * (3 + 2x)
(-3(3 + 2x) + 2x * (3 + 2x)) = 7
((3 * -3 + 2x * -3) + 2x * (3 + 2x)) = 7
((-9 + -6x) + 2x * (3 + 2x)) = 7
(-9 + -6x + (3 * 2x + 2x * 2x)) = 7
(-9 + -6x + (6x + 4x2)) = 7

Combine like terms: -6x + 6x = 0
(-9 + 0 + 4x2) = 7
(-9 + 4x2) = 7

Solving
-9 + 4x2 = 7

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + 4x2 = 7 + 9

Combine like terms: -9 + 9 = 0
0 + 4x2 = 7 + 9
4x2 = 7 + 9

Combine like terms: 7 + 9 = 16
4x2 = 16

Divide each side by '4'.
x2 = 4

Simplifying
x2 = 4

Take the square root of each side:
x = {-2, 2}