6x^2-63x=33

Solution for 6x^2-63x=33 equation:

Simplifying
6x2 + -63x = 33

Reorder the terms:
-63x + 6x2 = 33

Solving
-63x + 6x2 = 33

Solving for variable 'x'.

Reorder the terms:
-33 + -63x + 6x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + -63x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-11 + -21x + 2x2) = 0

Factor a trinomial.
3((-1 + -2x)(11 + -1x)) = 0

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-0.5, 11}