(2x+10)(x-2)=x^2+5x+112

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Solution for (2x+10)(x-2)=x^2+5x+112 equation: 


Simplifying
(2x + 10)(x + -2) = x2 + 5x + 112

Reorder the terms:
(10 + 2x)(x + -2) = x2 + 5x + 112

Reorder the terms:
(10 + 2x)(-2 + x) = x2 + 5x + 112

Multiply (10 + 2x) * (-2 + x)
(10(-2 + x) + 2x * (-2 + x)) = x2 + 5x + 112
((-2 * 10 + x * 10) + 2x * (-2 + x)) = x2 + 5x + 112
((-20 + 10x) + 2x * (-2 + x)) = x2 + 5x + 112
(-20 + 10x + (-2 * 2x + x * 2x)) = x2 + 5x + 112
(-20 + 10x + (-4x + 2x2)) = x2 + 5x + 112

Combine like terms: 10x + -4x = 6x
(-20 + 6x + 2x2) = x2 + 5x + 112

Reorder the terms:
-20 + 6x + 2x2 = 112 + 5x + x2

Solving
-20 + 6x + 2x2 = 112 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
-20 + -112 + 6x + -5x + 2x2 + -1x2 = 112 + 5x + x2 + -112 + -5x + -1x2

Combine like terms: -20 + -112 = -132
-132 + 6x + -5x + 2x2 + -1x2 = 112 + 5x + x2 + -112 + -5x + -1x2

Combine like terms: 6x + -5x = 1x
-132 + 1x + 2x2 + -1x2 = 112 + 5x + x2 + -112 + -5x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-132 + 1x + 1x2 = 112 + 5x + x2 + -112 + -5x + -1x2

Reorder the terms:
-132 + 1x + 1x2 = 112 + -112 + 5x + -5x + x2 + -1x2

Combine like terms: 112 + -112 = 0
-132 + 1x + 1x2 = 0 + 5x + -5x + x2 + -1x2
-132 + 1x + 1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
-132 + 1x + 1x2 = 0 + x2 + -1x2
-132 + 1x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-132 + 1x + 1x2 = 0

Factor a trinomial.
(-12 + -1x)(11 + -1x) = 0


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 '(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 = {-12, 11}

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