8-19x=8-12x+x^2

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Solution for 8-19x=8-12x+x^2 equation: 


Simplifying
8 + -19x = 8 + -12x + x2

Add '-8' to each side of the equation.
8 + -8 + -19x = 8 + -12x + -8 + x2

Combine like terms: 8 + -8 = 0
0 + -19x = 8 + -12x + -8 + x2
-19x = 8 + -12x + -8 + x2

Reorder the terms:
-19x = 8 + -8 + -12x + x2

Combine like terms: 8 + -8 = 0
-19x = 0 + -12x + x2
-19x = -12x + x2

Solving
-19x = -12x + x2

Solving for variable 'x'.

Combine like terms: -19x + 12x = -7x
-7x + -1x2 = -12x + x2 + 12x + -1x2

Reorder the terms:
-7x + -1x2 = -12x + 12x + x2 + -1x2

Combine like terms: -12x + 12x = 0
-7x + -1x2 = 0 + x2 + -1x2
-7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(7 + x) = 0

Ignore the factor -1.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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 = {0, -7}

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