(x-2)(4+x)=112

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Solution for (x-2)(4+x)=112 equation:


Simplifying
(x + -2)(4 + x) = 112

Reorder the terms:
(-2 + x)(4 + x) = 112

Multiply (-2 + x) * (4 + x)
(-2(4 + x) + x(4 + x)) = 112
((4 * -2 + x * -2) + x(4 + x)) = 112
((-8 + -2x) + x(4 + x)) = 112
(-8 + -2x + (4 * x + x * x)) = 112
(-8 + -2x + (4x + x2)) = 112

Combine like terms: -2x + 4x = 2x
(-8 + 2x + x2) = 112

Solving
-8 + 2x + x2 = 112

Solving for variable 'x'.

Reorder the terms:
-8 + -112 + 2x + x2 = 112 + -112

Combine like terms: -8 + -112 = -120
-120 + 2x + x2 = 112 + -112

Combine like terms: 112 + -112 = 0
-120 + 2x + x2 = 0

Factor a trinomial.
(-12 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-12, 10}

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