-33=-3x^2+6x+12

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Solution for -33=-3x^2+6x+12 equation: 


Simplifying
-33 = -3x2 + 6x + 12

Reorder the terms:
-33 = 12 + 6x + -3x2

Solving
-33 = 12 + 6x + -3x2

Solving for variable 'x'.

Combine like terms: -33 + -12 = -45
-45 + -6x + 3x2 = 12 + 6x + -3x2 + -12 + -6x + 3x2

Reorder the terms:
-45 + -6x + 3x2 = 12 + -12 + 6x + -6x + -3x2 + 3x2

Combine like terms: 12 + -12 = 0
-45 + -6x + 3x2 = 0 + 6x + -6x + -3x2 + 3x2
-45 + -6x + 3x2 = 6x + -6x + -3x2 + 3x2

Combine like terms: 6x + -6x = 0
-45 + -6x + 3x2 = 0 + -3x2 + 3x2
-45 + -6x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-45 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -2x + x2) = 0

Factor a trinomial.
3((-3 + -1x)(5 + -1x)) = 0

Ignore the factor 3.

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 '(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
Solution
x = {-3, 5}

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