x^2-x-19=-5x+2

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Solution for x^2-x-19=-5x+2 equation: 


Simplifying
x2 + -1x + -19 = -5x + 2

Reorder the terms:
-19 + -1x + x2 = -5x + 2

Reorder the terms:
-19 + -1x + x2 = 2 + -5x

Solving
-19 + -1x + x2 = 2 + -5x

Solving for variable 'x'.

Reorder the terms:
-19 + -2 + -1x + 5x + x2 = 2 + -5x + -2 + 5x

Combine like terms: -19 + -2 = -21
-21 + -1x + 5x + x2 = 2 + -5x + -2 + 5x

Combine like terms: -1x + 5x = 4x
-21 + 4x + x2 = 2 + -5x + -2 + 5x

Reorder the terms:
-21 + 4x + x2 = 2 + -2 + -5x + 5x

Combine like terms: 2 + -2 = 0
-21 + 4x + x2 = 0 + -5x + 5x
-21 + 4x + x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-21 + 4x + x2 = 0

Factor a trinomial.
(-7 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-7, 3}

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