0=(3x^2)-33x+90

Solution for 0=(3x^2)-33x+90 equation:

Simplifying
0 = (3x2) + -33x + 90

Reorder the terms:
0 = 90 + -33x + (3x2)

Solving
0 = 90 + -33x + (3x2)

Solving for variable 'x'.

Combine like terms: 0 + -90 = -90
-90 + 33x + (-3x2) = 90 + -33x + (3x2) + -90 + 33x + (-3x2)

Reorder the terms:
-90 + 33x + (-3x2) = 90 + -90 + -33x + 33x + (3x2) + (-3x2)

Combine like terms: 90 + -90 = 0
-90 + 33x + (-3x2) = 0 + -33x + 33x + (3x2) + (-3x2)
-90 + 33x + (-3x2) = -33x + 33x + (3x2) + (-3x2)

Combine like terms: -33x + 33x = 0
-90 + 33x + (-3x2) = 0 + (3x2) + (-3x2)
-90 + 33x + (-3x2) = (3x2) + (-3x2)

Combine like terms: (3x2) + (-3x2) = 0
-90 + 33x + (-3x2) = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + 11x + (-1x2)) = 0

Factor a trinomial.
3((-6 + x)(5 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

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

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
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 = {6, 5}