3(x+4)(x+4)-5=22

Solution for 3(x+4)(x+4)-5=22 equation:

Simplifying
3(x + 4)(x + 4) + -5 = 22

Reorder the terms:
3(4 + x)(x + 4) + -5 = 22

Reorder the terms:
3(4 + x)(4 + x) + -5 = 22

Multiply (4 + x) * (4 + x)
3(4(4 + x) + x(4 + x)) + -5 = 22
3((4 * 4 + x * 4) + x(4 + x)) + -5 = 22
3((16 + 4x) + x(4 + x)) + -5 = 22
3(16 + 4x + (4 * x + x * x)) + -5 = 22
3(16 + 4x + (4x + x2)) + -5 = 22

Combine like terms: 4x + 4x = 8x
3(16 + 8x + x2) + -5 = 22
(16 * 3 + 8x * 3 + x2 * 3) + -5 = 22
(48 + 24x + 3x2) + -5 = 22

Reorder the terms:
48 + -5 + 24x + 3x2 = 22

Combine like terms: 48 + -5 = 43
43 + 24x + 3x2 = 22

Solving
43 + 24x + 3x2 = 22

Solving for variable 'x'.

Reorder the terms:
43 + -22 + 24x + 3x2 = 22 + -22

Combine like terms: 43 + -22 = 21
21 + 24x + 3x2 = 22 + -22

Combine like terms: 22 + -22 = 0
21 + 24x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + 8x + x2) = 0

Factor a trinomial.
3((7 + x)(1 + x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
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 = {-7, -1}