(x+4)(x+4)+6=87

Solution for (x+4)(x+4)+6=87 equation:

Simplifying
(x + 4)(x + 4) + 6 = 87

Reorder the terms:
(4 + x)(x + 4) + 6 = 87

Reorder the terms:
(4 + x)(4 + x) + 6 = 87

Multiply (4 + x) * (4 + x)
(4(4 + x) + x(4 + x)) + 6 = 87
((4 * 4 + x * 4) + x(4 + x)) + 6 = 87
((16 + 4x) + x(4 + x)) + 6 = 87
(16 + 4x + (4 * x + x * x)) + 6 = 87
(16 + 4x + (4x + x2)) + 6 = 87

Combine like terms: 4x + 4x = 8x
(16 + 8x + x2) + 6 = 87

Reorder the terms:
16 + 6 + 8x + x2 = 87

Combine like terms: 16 + 6 = 22
22 + 8x + x2 = 87

Solving
22 + 8x + x2 = 87

Solving for variable 'x'.

Reorder the terms:
22 + -87 + 8x + x2 = 87 + -87

Combine like terms: 22 + -87 = -65
-65 + 8x + x2 = 87 + -87

Combine like terms: 87 + -87 = 0
-65 + 8x + x2 = 0

Factor a trinomial.
(-13 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13
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 = {-13, 5}