3x^2-3x=90

Solution for 3x^2-3x=90 equation:

Simplifying
3x2 + -3x = 90

Reorder the terms:
-3x + 3x2 = 90

Solving
-3x + 3x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + -3x + 3x2 = 90 + -90

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

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

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-5, 6}