5x^2-45x=-90

Solution for 5x^2-45x=-90 equation:

Simplifying
5x2 + -45x = -90

Reorder the terms:
-45x + 5x2 = -90

Solving
-45x + 5x2 = -90

Solving for variable 'x'.

Reorder the terms:
90 + -45x + 5x2 = -90 + 90

Combine like terms: -90 + 90 = 0
90 + -45x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(18 + -9x + x2) = 0

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

Ignore the factor 5.
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 '(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 = {3, 6}