x^2-13=-6x+3

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Solution for x^2-13=-6x+3 equation: 


Simplifying
x2 + -13 = -6x + 3

Reorder the terms:
-13 + x2 = -6x + 3

Reorder the terms:
-13 + x2 = 3 + -6x

Solving
-13 + x2 = 3 + -6x

Solving for variable 'x'.

Reorder the terms:
-13 + -3 + 6x + x2 = 3 + -6x + -3 + 6x

Combine like terms: -13 + -3 = -16
-16 + 6x + x2 = 3 + -6x + -3 + 6x

Reorder the terms:
-16 + 6x + x2 = 3 + -3 + -6x + 6x

Combine like terms: 3 + -3 = 0
-16 + 6x + x2 = 0 + -6x + 6x
-16 + 6x + x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-16 + 6x + x2 = 0

Factor a trinomial.
(-8 + -1x)(2 + -1x) = 0


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

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-8, 2}

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