(6+2x)(12+2x)=160

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Solution for (6+2x)(12+2x)=160 equation: 


Simplifying
(6 + 2x)(12 + 2x) = 160

Multiply (6 + 2x) * (12 + 2x)
(6(12 + 2x) + 2x * (12 + 2x)) = 160
((12 * 6 + 2x * 6) + 2x * (12 + 2x)) = 160
((72 + 12x) + 2x * (12 + 2x)) = 160
(72 + 12x + (12 * 2x + 2x * 2x)) = 160
(72 + 12x + (24x + 4x2)) = 160

Combine like terms: 12x + 24x = 36x
(72 + 36x + 4x2) = 160

Solving
72 + 36x + 4x2 = 160

Solving for variable 'x'.

Reorder the terms:
72 + -160 + 36x + 4x2 = 160 + -160

Combine like terms: 72 + -160 = -88
-88 + 36x + 4x2 = 160 + -160

Combine like terms: 160 + -160 = 0
-88 + 36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-22 + 9x + x2) = 0

Factor a trinomial.
4((-11 + -1x)(2 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11

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 = {-11, 2}

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