6x^2+12x-13=15-5x

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Solution for 6x^2+12x-13=15-5x equation: 


Simplifying
6x2 + 12x + -13 = 15 + -5x

Reorder the terms:
-13 + 12x + 6x2 = 15 + -5x

Solving
-13 + 12x + 6x2 = 15 + -5x

Solving for variable 'x'.

Reorder the terms:
-13 + -15 + 12x + 5x + 6x2 = 15 + -5x + -15 + 5x

Combine like terms: -13 + -15 = -28
-28 + 12x + 5x + 6x2 = 15 + -5x + -15 + 5x

Combine like terms: 12x + 5x = 17x
-28 + 17x + 6x2 = 15 + -5x + -15 + 5x

Reorder the terms:
-28 + 17x + 6x2 = 15 + -15 + -5x + 5x

Combine like terms: 15 + -15 = 0
-28 + 17x + 6x2 = 0 + -5x + 5x
-28 + 17x + 6x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-28 + 17x + 6x2 = 0

Factor a trinomial.
(-4 + -1x)(7 + -6x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 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 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {-4, 1.166666667}

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