(6+2x)(5+2x)=72

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Solution for (6+2x)(5+2x)=72 equation: 


Simplifying
(6 + 2x)(5 + 2x) = 72

Multiply (6 + 2x) * (5 + 2x)
(6(5 + 2x) + 2x * (5 + 2x)) = 72
((5 * 6 + 2x * 6) + 2x * (5 + 2x)) = 72
((30 + 12x) + 2x * (5 + 2x)) = 72
(30 + 12x + (5 * 2x + 2x * 2x)) = 72
(30 + 12x + (10x + 4x2)) = 72

Combine like terms: 12x + 10x = 22x
(30 + 22x + 4x2) = 72

Solving
30 + 22x + 4x2 = 72

Solving for variable 'x'.

Reorder the terms:
30 + -72 + 22x + 4x2 = 72 + -72

Combine like terms: 30 + -72 = -42
-42 + 22x + 4x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-42 + 22x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 11x + 2x2) = 0

Factor a trinomial.
2((-7 + -1x)(3 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-7, 1.5}

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