2(x+4)(x+4)=338

Solution for 2(x+4)(x+4)=338 equation:

Simplifying
2(x + 4)(x + 4) = 338

Reorder the terms:
2(4 + x)(x + 4) = 338

Reorder the terms:
2(4 + x)(4 + x) = 338

Multiply (4 + x) * (4 + x)
2(4(4 + x) + x(4 + x)) = 338
2((4 * 4 + x * 4) + x(4 + x)) = 338
2((16 + 4x) + x(4 + x)) = 338
2(16 + 4x + (4 * x + x * x)) = 338
2(16 + 4x + (4x + x2)) = 338

Combine like terms: 4x + 4x = 8x
2(16 + 8x + x2) = 338
(16 * 2 + 8x * 2 + x2 * 2) = 338
(32 + 16x + 2x2) = 338

Solving
32 + 16x + 2x2 = 338

Solving for variable 'x'.

Reorder the terms:
32 + -338 + 16x + 2x2 = 338 + -338

Combine like terms: 32 + -338 = -306
-306 + 16x + 2x2 = 338 + -338

Combine like terms: 338 + -338 = 0
-306 + 16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-153 + 8x + x2) = 0

Factor a trinomial.
2((-17 + -1x)(9 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve:

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-17, 9}