x^2-8x+14-7+5a-3a-2a=112

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Solution for x^2-8x+14-7+5a-3a-2a=112 equation: 


Simplifying
x2 + -8x + 14 + -7 + 5a + -3a + -2a = 112

Reorder the terms:
14 + -7 + 5a + -3a + -2a + -8x + x2 = 112

Combine like terms: 14 + -7 = 7
7 + 5a + -3a + -2a + -8x + x2 = 112

Combine like terms: 5a + -3a = 2a
7 + 2a + -2a + -8x + x2 = 112

Combine like terms: 2a + -2a = 0
7 + 0 + -8x + x2 = 112
7 + -8x + x2 = 112

Solving
7 + -8x + x2 = 112

Solving for variable 'x'.

Reorder the terms:
7 + -112 + -8x + x2 = 112 + -112

Combine like terms: 7 + -112 = -105
-105 + -8x + x2 = 112 + -112

Combine like terms: 112 + -112 = 0
-105 + -8x + x2 = 0

Factor a trinomial.
(-7 + -1x)(15 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-7, 15}

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