x^2-3x-13=6x-21

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Solution for x^2-3x-13=6x-21 equation: 


Simplifying
x2 + -3x + -13 = 6x + -21

Reorder the terms:
-13 + -3x + x2 = 6x + -21

Reorder the terms:
-13 + -3x + x2 = -21 + 6x

Solving
-13 + -3x + x2 = -21 + 6x

Solving for variable 'x'.

Reorder the terms:
-13 + 21 + -3x + -6x + x2 = -21 + 6x + 21 + -6x

Combine like terms: -13 + 21 = 8
8 + -3x + -6x + x2 = -21 + 6x + 21 + -6x

Combine like terms: -3x + -6x = -9x
8 + -9x + x2 = -21 + 6x + 21 + -6x

Reorder the terms:
8 + -9x + x2 = -21 + 21 + 6x + -6x

Combine like terms: -21 + 21 = 0
8 + -9x + x2 = 0 + 6x + -6x
8 + -9x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
8 + -9x + x2 = 0

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


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
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
Solution
x = {1, 8}

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