9x-12=(x-2)(x+2)

Solution for 9x-12=(x-2)(x+2) equation:

Simplifying
9x + -12 = (x + -2)(x + 2)

Reorder the terms:
-12 + 9x = (x + -2)(x + 2)

Reorder the terms:
-12 + 9x = (-2 + x)(x + 2)

Reorder the terms:
-12 + 9x = (-2 + x)(2 + x)

Multiply (-2 + x) * (2 + x)
-12 + 9x = (-2(2 + x) + x(2 + x))
-12 + 9x = ((2 * -2 + x * -2) + x(2 + x))
-12 + 9x = ((-4 + -2x) + x(2 + x))
-12 + 9x = (-4 + -2x + (2 * x + x * x))
-12 + 9x = (-4 + -2x + (2x + x2))

Combine like terms: -2x + 2x = 0
-12 + 9x = (-4 + 0 + x2)
-12 + 9x = (-4 + x2)

Solving
-12 + 9x = -4 + x2

Solving for variable 'x'.

Reorder the terms:
-12 + 4 + 9x + -1x2 = -4 + x2 + 4 + -1x2

Combine like terms: -12 + 4 = -8
-8 + 9x + -1x2 = -4 + x2 + 4 + -1x2

Reorder the terms:
-8 + 9x + -1x2 = -4 + 4 + x2 + -1x2

Combine like terms: -4 + 4 = 0
-8 + 9x + -1x2 = 0 + x2 + -1x2
-8 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + 9x + -1x2 = 0

Factor a trinomial.
(-8 + x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {8, 1}