(12-2x)(16-2x)=60

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Solution for (12-2x)(16-2x)=60 equation: 


Simplifying
(12 + -2x)(16 + -2x) = 60

Multiply (12 + -2x) * (16 + -2x)
(12(16 + -2x) + -2x * (16 + -2x)) = 60
((16 * 12 + -2x * 12) + -2x * (16 + -2x)) = 60
((192 + -24x) + -2x * (16 + -2x)) = 60
(192 + -24x + (16 * -2x + -2x * -2x)) = 60
(192 + -24x + (-32x + 4x2)) = 60

Combine like terms: -24x + -32x = -56x
(192 + -56x + 4x2) = 60

Solving
192 + -56x + 4x2 = 60

Solving for variable 'x'.

Reorder the terms:
192 + -60 + -56x + 4x2 = 60 + -60

Combine like terms: 192 + -60 = 132
132 + -56x + 4x2 = 60 + -60

Combine like terms: 60 + -60 = 0
132 + -56x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(33 + -14x + x2) = 0

Factor a trinomial.
4((3 + -1x)(11 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
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
Solution
x = {3, 11}

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