(13-2x)(22-2x)=112

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Solution for (13-2x)(22-2x)=112 equation: 


Simplifying
(13 + -2x)(22 + -2x) = 112

Multiply (13 + -2x) * (22 + -2x)
(13(22 + -2x) + -2x * (22 + -2x)) = 112
((22 * 13 + -2x * 13) + -2x * (22 + -2x)) = 112
((286 + -26x) + -2x * (22 + -2x)) = 112
(286 + -26x + (22 * -2x + -2x * -2x)) = 112
(286 + -26x + (-44x + 4x2)) = 112

Combine like terms: -26x + -44x = -70x
(286 + -70x + 4x2) = 112

Solving
286 + -70x + 4x2 = 112

Solving for variable 'x'.

Reorder the terms:
286 + -112 + -70x + 4x2 = 112 + -112

Combine like terms: 286 + -112 = 174
174 + -70x + 4x2 = 112 + -112

Combine like terms: 112 + -112 = 0
174 + -70x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(87 + -35x + 2x2) = 0

Factor a trinomial.
2((3 + -1x)(29 + -2x)) = 0

Ignore the factor 2.

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 '(29 + -2x)' equal to zero and attempt to solve:

Simplifying
29 + -2x = 0

Solving
29 + -2x = 0

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

Add '-29' to each side of the equation.
29 + -29 + -2x = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -2x = 0 + -29
-2x = 0 + -29

Combine like terms: 0 + -29 = -29
-2x = -29

Divide each side by '-2'.
x = 14.5

Simplifying
x = 14.5
Solution
x = {3, 14.5}

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