9((4x-4)+9)=9x^2

Solution for 9((4x-4)+9)=9x^2 equation:

Simplifying
9((4x + -4) + 9) = 9x2

Reorder the terms:
9((-4 + 4x) + 9) = 9x2

Remove parenthesis around (-4 + 4x)
9(-4 + 4x + 9) = 9x2

Reorder the terms:
9(-4 + 9 + 4x) = 9x2

Combine like terms: -4 + 9 = 5
9(5 + 4x) = 9x2
(5 * 9 + 4x * 9) = 9x2
(45 + 36x) = 9x2

Solving
45 + 36x = 9x2

Solving for variable 'x'.

Combine like terms: 9x2 + -9x2 = 0
45 + 36x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(5 + 4x + -1x2) = 0

Factor a trinomial.
9((5 + -1x)(1 + x)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {5, -1}