6x^2+11x-16=x+8

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Solution for 6x^2+11x-16=x+8 equation: 


Simplifying
6x2 + 11x + -16 = x + 8

Reorder the terms:
-16 + 11x + 6x2 = x + 8

Reorder the terms:
-16 + 11x + 6x2 = 8 + x

Solving
-16 + 11x + 6x2 = 8 + x

Solving for variable 'x'.

Reorder the terms:
-16 + -8 + 11x + -1x + 6x2 = 8 + x + -8 + -1x

Combine like terms: -16 + -8 = -24
-24 + 11x + -1x + 6x2 = 8 + x + -8 + -1x

Combine like terms: 11x + -1x = 10x
-24 + 10x + 6x2 = 8 + x + -8 + -1x

Reorder the terms:
-24 + 10x + 6x2 = 8 + -8 + x + -1x

Combine like terms: 8 + -8 = 0
-24 + 10x + 6x2 = 0 + x + -1x
-24 + 10x + 6x2 = x + -1x

Combine like terms: x + -1x = 0
-24 + 10x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 5x + 3x2) = 0

Factor a trinomial.
2((-3 + -1x)(4 + -3x)) = 0

Ignore the factor 2.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-3, 1.333333333}

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