x^2-9x+76=20-24x

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Solution for x^2-9x+76=20-24x equation: 


Simplifying
x2 + -9x + 76 = 20 + -24x

Reorder the terms:
76 + -9x + x2 = 20 + -24x

Solving
76 + -9x + x2 = 20 + -24x

Solving for variable 'x'.

Reorder the terms:
76 + -20 + -9x + 24x + x2 = 20 + -24x + -20 + 24x

Combine like terms: 76 + -20 = 56
56 + -9x + 24x + x2 = 20 + -24x + -20 + 24x

Combine like terms: -9x + 24x = 15x
56 + 15x + x2 = 20 + -24x + -20 + 24x

Reorder the terms:
56 + 15x + x2 = 20 + -20 + -24x + 24x

Combine like terms: 20 + -20 = 0
56 + 15x + x2 = 0 + -24x + 24x
56 + 15x + x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
56 + 15x + x2 = 0

Factor a trinomial.
(8 + x)(7 + x) = 0


Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

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

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

Simplifying
x = -7
Solution
x = {-8, -7}

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