(5+2x)(15+2x)=231

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Solution for (5+2x)(15+2x)=231 equation: 


Simplifying
(5 + 2x)(15 + 2x) = 231

Multiply (5 + 2x) * (15 + 2x)
(5(15 + 2x) + 2x * (15 + 2x)) = 231
((15 * 5 + 2x * 5) + 2x * (15 + 2x)) = 231
((75 + 10x) + 2x * (15 + 2x)) = 231
(75 + 10x + (15 * 2x + 2x * 2x)) = 231
(75 + 10x + (30x + 4x2)) = 231

Combine like terms: 10x + 30x = 40x
(75 + 40x + 4x2) = 231

Solving
75 + 40x + 4x2 = 231

Solving for variable 'x'.

Reorder the terms:
75 + -231 + 40x + 4x2 = 231 + -231

Combine like terms: 75 + -231 = -156
-156 + 40x + 4x2 = 231 + -231

Combine like terms: 231 + -231 = 0
-156 + 40x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-39 + 10x + x2) = 0

Factor a trinomial.
4((-13 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

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}

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