(10+2x)(15+2x)-150=116

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Solution for (10+2x)(15+2x)-150=116 equation: 


Simplifying
(10 + 2x)(15 + 2x) + -150 = 116

Multiply (10 + 2x) * (15 + 2x)
(10(15 + 2x) + 2x * (15 + 2x)) + -150 = 116
((15 * 10 + 2x * 10) + 2x * (15 + 2x)) + -150 = 116
((150 + 20x) + 2x * (15 + 2x)) + -150 = 116
(150 + 20x + (15 * 2x + 2x * 2x)) + -150 = 116
(150 + 20x + (30x + 4x2)) + -150 = 116

Combine like terms: 20x + 30x = 50x
(150 + 50x + 4x2) + -150 = 116

Reorder the terms:
150 + -150 + 50x + 4x2 = 116

Combine like terms: 150 + -150 = 0
0 + 50x + 4x2 = 116
50x + 4x2 = 116

Solving
50x + 4x2 = 116

Solving for variable 'x'.

Reorder the terms:
-116 + 50x + 4x2 = 116 + -116

Combine like terms: 116 + -116 = 0
-116 + 50x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-58 + 25x + 2x2) = 0

Factor a trinomial.
2((-29 + -2x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-29 + -2x)' equal to zero and attempt to solve:

Simplifying
-29 + -2x = 0

Solving
-29 + -2x = 0

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

Add '29' to each side of the equation.
-29 + 29 + -2x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -2x = 0 + 29
-2x = 0 + 29

Combine like terms: 0 + 29 = 29
-2x = 29

Divide each side by '-2'.
x = -14.5

Simplifying
x = -14.5

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 = {-14.5, 2}

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