2(x+5)(x+5)+10=138

Solution for 2(x+5)(x+5)+10=138 equation:

Simplifying
2(x + 5)(x + 5) + 10 = 138

Reorder the terms:
2(5 + x)(x + 5) + 10 = 138

Reorder the terms:
2(5 + x)(5 + x) + 10 = 138

Multiply (5 + x) * (5 + x)
2(5(5 + x) + x(5 + x)) + 10 = 138
2((5 * 5 + x * 5) + x(5 + x)) + 10 = 138
2((25 + 5x) + x(5 + x)) + 10 = 138
2(25 + 5x + (5 * x + x * x)) + 10 = 138
2(25 + 5x + (5x + x2)) + 10 = 138

Combine like terms: 5x + 5x = 10x
2(25 + 10x + x2) + 10 = 138
(25 * 2 + 10x * 2 + x2 * 2) + 10 = 138
(50 + 20x + 2x2) + 10 = 138

Reorder the terms:
50 + 10 + 20x + 2x2 = 138

Combine like terms: 50 + 10 = 60
60 + 20x + 2x2 = 138

Solving
60 + 20x + 2x2 = 138

Solving for variable 'x'.

Reorder the terms:
60 + -138 + 20x + 2x2 = 138 + -138

Combine like terms: 60 + -138 = -78
-78 + 20x + 2x2 = 138 + -138

Combine like terms: 138 + -138 = 0
-78 + 20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-39 + 10x + x2) = 0

Factor a trinomial.
2((-13 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-13, 3}