3x^2-33x=78

Solution for 3x^2-33x=78 equation:

Simplifying
3x2 + -33x = 78

Reorder the terms:
-33x + 3x2 = 78

Solving
-33x + 3x2 = 78

Solving for variable 'x'.

Reorder the terms:
-78 + -33x + 3x2 = 78 + -78

Combine like terms: 78 + -78 = 0
-78 + -33x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-26 + -11x + x2) = 0

Factor a trinomial.
3((-2 + -1x)(13 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-2, 13}