(10+2x)(12+2x)=168

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Solution for (10+2x)(12+2x)=168 equation: 


Simplifying
(10 + 2x)(12 + 2x) = 168

Multiply (10 + 2x) * (12 + 2x)
(10(12 + 2x) + 2x * (12 + 2x)) = 168
((12 * 10 + 2x * 10) + 2x * (12 + 2x)) = 168
((120 + 20x) + 2x * (12 + 2x)) = 168
(120 + 20x + (12 * 2x + 2x * 2x)) = 168
(120 + 20x + (24x + 4x2)) = 168

Combine like terms: 20x + 24x = 44x
(120 + 44x + 4x2) = 168

Solving
120 + 44x + 4x2 = 168

Solving for variable 'x'.

Reorder the terms:
120 + -168 + 44x + 4x2 = 168 + -168

Combine like terms: 120 + -168 = -48
-48 + 44x + 4x2 = 168 + -168

Combine like terms: 168 + -168 = 0
-48 + 44x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + 11x + x2) = 0

Factor a trinomial.
4((-12 + -1x)(1 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-12, 1}

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