0=6x^2-6x-36

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Solution for 0=6x^2-6x-36 equation: 


Simplifying
0 = 6x2 + -6x + -36

Reorder the terms:
0 = -36 + -6x + 6x2

Solving
0 = -36 + -6x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 36 = 36
36 + 6x + -6x2 = -36 + -6x + 6x2 + 36 + 6x + -6x2

Reorder the terms:
36 + 6x + -6x2 = -36 + 36 + -6x + 6x + 6x2 + -6x2

Combine like terms: -36 + 36 = 0
36 + 6x + -6x2 = 0 + -6x + 6x + 6x2 + -6x2
36 + 6x + -6x2 = -6x + 6x + 6x2 + -6x2

Combine like terms: -6x + 6x = 0
36 + 6x + -6x2 = 0 + 6x2 + -6x2
36 + 6x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
36 + 6x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + x + -1x2) = 0

Factor a trinomial.
6((3 + -1x)(2 + x)) = 0

Ignore the factor 6.

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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {3, -2}

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