(2x+12)(2x+10)=360

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Solution for (2x+12)(2x+10)=360 equation: 


Simplifying
(2x + 12)(2x + 10) = 360

Reorder the terms:
(12 + 2x)(2x + 10) = 360

Reorder the terms:
(12 + 2x)(10 + 2x) = 360

Multiply (12 + 2x) * (10 + 2x)
(12(10 + 2x) + 2x * (10 + 2x)) = 360
((10 * 12 + 2x * 12) + 2x * (10 + 2x)) = 360
((120 + 24x) + 2x * (10 + 2x)) = 360
(120 + 24x + (10 * 2x + 2x * 2x)) = 360
(120 + 24x + (20x + 4x2)) = 360

Combine like terms: 24x + 20x = 44x
(120 + 44x + 4x2) = 360

Solving
120 + 44x + 4x2 = 360

Solving for variable 'x'.

Reorder the terms:
120 + -360 + 44x + 4x2 = 360 + -360

Combine like terms: 120 + -360 = -240
-240 + 44x + 4x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-240 + 44x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-60 + 11x + x2) = 0

Factor a trinomial.
4((-15 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-15, 4}

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