6x^2+20x-13=22-3x

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Solution for 6x^2+20x-13=22-3x equation: 


Simplifying
6x2 + 20x + -13 = 22 + -3x

Reorder the terms:
-13 + 20x + 6x2 = 22 + -3x

Solving
-13 + 20x + 6x2 = 22 + -3x

Solving for variable 'x'.

Reorder the terms:
-13 + -22 + 20x + 3x + 6x2 = 22 + -3x + -22 + 3x

Combine like terms: -13 + -22 = -35
-35 + 20x + 3x + 6x2 = 22 + -3x + -22 + 3x

Combine like terms: 20x + 3x = 23x
-35 + 23x + 6x2 = 22 + -3x + -22 + 3x

Reorder the terms:
-35 + 23x + 6x2 = 22 + -22 + -3x + 3x

Combine like terms: 22 + -22 = 0
-35 + 23x + 6x2 = 0 + -3x + 3x
-35 + 23x + 6x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-35 + 23x + 6x2 = 0

Factor a trinomial.
(-5 + -1x)(7 + -6x) = 0


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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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 = {-5, 1.166666667}

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