2(x+3)(x+3)-9=89

Solution for 2(x+3)(x+3)-9=89 equation:

Simplifying
2(x + 3)(x + 3) + -9 = 89

Reorder the terms:
2(3 + x)(x + 3) + -9 = 89

Reorder the terms:
2(3 + x)(3 + x) + -9 = 89

Multiply (3 + x) * (3 + x)
2(3(3 + x) + x(3 + x)) + -9 = 89
2((3 * 3 + x * 3) + x(3 + x)) + -9 = 89
2((9 + 3x) + x(3 + x)) + -9 = 89
2(9 + 3x + (3 * x + x * x)) + -9 = 89
2(9 + 3x + (3x + x2)) + -9 = 89

Combine like terms: 3x + 3x = 6x
2(9 + 6x + x2) + -9 = 89
(9 * 2 + 6x * 2 + x2 * 2) + -9 = 89
(18 + 12x + 2x2) + -9 = 89

Reorder the terms:
18 + -9 + 12x + 2x2 = 89

Combine like terms: 18 + -9 = 9
9 + 12x + 2x2 = 89

Solving
9 + 12x + 2x2 = 89

Solving for variable 'x'.

Reorder the terms:
9 + -89 + 12x + 2x2 = 89 + -89

Combine like terms: 9 + -89 = -80
-80 + 12x + 2x2 = 89 + -89

Combine like terms: 89 + -89 = 0
-80 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + 6x + x2) = 0

Factor a trinomial.
2((-10 + -1x)(4 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-10, 4}