6x^2+7x-12=37-28x

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Solution for 6x^2+7x-12=37-28x equation: 


Simplifying
6x2 + 7x + -12 = 37 + -28x

Reorder the terms:
-12 + 7x + 6x2 = 37 + -28x

Solving
-12 + 7x + 6x2 = 37 + -28x

Solving for variable 'x'.

Reorder the terms:
-12 + -37 + 7x + 28x + 6x2 = 37 + -28x + -37 + 28x

Combine like terms: -12 + -37 = -49
-49 + 7x + 28x + 6x2 = 37 + -28x + -37 + 28x

Combine like terms: 7x + 28x = 35x
-49 + 35x + 6x2 = 37 + -28x + -37 + 28x

Reorder the terms:
-49 + 35x + 6x2 = 37 + -37 + -28x + 28x

Combine like terms: 37 + -37 = 0
-49 + 35x + 6x2 = 0 + -28x + 28x
-49 + 35x + 6x2 = -28x + 28x

Combine like terms: -28x + 28x = 0
-49 + 35x + 6x2 = 0

Factor a trinomial.
(-7 + -1x)(7 + -6x) = 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 '(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 = {-7, 1.166666667}

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