(2x-5)+(6x^2-6x-11)=

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Solution for (2x-5)+(6x^2-6x-11)= equation: 


Simplifying
(2x + -5) + (6x2 + -6x + -11) = 0

Reorder the terms:
(-5 + 2x) + (6x2 + -6x + -11) = 0

Remove parenthesis around (-5 + 2x)
-5 + 2x + (6x2 + -6x + -11) = 0

Reorder the terms:
-5 + 2x + (-11 + -6x + 6x2) = 0

Remove parenthesis around (-11 + -6x + 6x2)
-5 + 2x + -11 + -6x + 6x2 = 0

Reorder the terms:
-5 + -11 + 2x + -6x + 6x2 = 0

Combine like terms: -5 + -11 = -16
-16 + 2x + -6x + 6x2 = 0

Combine like terms: 2x + -6x = -4x
-16 + -4x + 6x2 = 0

Solving
-16 + -4x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -2x + 3x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1.333333333, 2}

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