x^2+(x+3)*(x+3)=89

Solution for x^2+(x+3)*(x+3)=89 equation:

Simplifying
x2 + (x + 3)(x + 3) = 89

Reorder the terms:
x2 + (3 + x)(x + 3) = 89

Reorder the terms:
x2 + (3 + x)(3 + x) = 89

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

Combine like terms: 3x + 3x = 6x
x2 + (9 + 6x + x2) = 89

Reorder the terms:
9 + 6x + x2 + x2 = 89

Combine like terms: x2 + x2 = 2x2
9 + 6x + 2x2 = 89

Solving
9 + 6x + 2x2 = 89

Solving for variable 'x'.

Reorder the terms:
9 + -89 + 6x + 2x2 = 89 + -89

Combine like terms: 9 + -89 = -80
-80 + 6x + 2x2 = 89 + -89

Combine like terms: 89 + -89 = 0
-80 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + 3x + x2) = 0

Factor a trinomial.
2((-8 + -1x)(5 + -1x)) = 0

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

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

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

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

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
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
Solution
x = {-8, 5}