3x^2-6x-13=x+7

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Solution for 3x^2-6x-13=x+7 equation: 


Simplifying
3x2 + -6x + -13 = x + 7

Reorder the terms:
-13 + -6x + 3x2 = x + 7

Reorder the terms:
-13 + -6x + 3x2 = 7 + x

Solving
-13 + -6x + 3x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-13 + -7 + -6x + -1x + 3x2 = 7 + x + -7 + -1x

Combine like terms: -13 + -7 = -20
-20 + -6x + -1x + 3x2 = 7 + x + -7 + -1x

Combine like terms: -6x + -1x = -7x
-20 + -7x + 3x2 = 7 + x + -7 + -1x

Reorder the terms:
-20 + -7x + 3x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
-20 + -7x + 3x2 = 0 + x + -1x
-20 + -7x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
-20 + -7x + 3x2 = 0

Factor a trinomial.
(-5 + -3x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1.666666667, 4}

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