2((x+4)(x+4))-18=54

Solution for 2((x+4)(x+4))-18=54 equation:

Simplifying
2((x + 4)(x + 4)) + -18 = 54

Reorder the terms:
2((4 + x)(x + 4)) + -18 = 54

Reorder the terms:
2((4 + x)(4 + x)) + -18 = 54

Multiply (4 + x) * (4 + x)
2((4(4 + x) + x(4 + x))) + -18 = 54
2(((4 * 4 + x * 4) + x(4 + x))) + -18 = 54
2(((16 + 4x) + x(4 + x))) + -18 = 54
2((16 + 4x + (4 * x + x * x))) + -18 = 54
2((16 + 4x + (4x + x2))) + -18 = 54

Combine like terms: 4x + 4x = 8x
2((16 + 8x + x2)) + -18 = 54
(16 * 2 + 8x * 2 + x2 * 2) + -18 = 54
(32 + 16x + 2x2) + -18 = 54

Reorder the terms:
32 + -18 + 16x + 2x2 = 54

Combine like terms: 32 + -18 = 14
14 + 16x + 2x2 = 54

Solving
14 + 16x + 2x2 = 54

Solving for variable 'x'.

Reorder the terms:
14 + -54 + 16x + 2x2 = 54 + -54

Combine like terms: 14 + -54 = -40
-40 + 16x + 2x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-40 + 16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 8x + x2) = 0

Factor a trinomial.
2((-10 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-10, 2}