-15X^2-75X+90=0

Solution for -15X^2-75X+90=0 equation:

Simplifying
-15X2 + -75X + 90 = 0

Reorder the terms:
90 + -75X + -15X2 = 0

Solving
90 + -75X + -15X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '15'.
15(6 + -5X + -1X2) = 0

Factor a trinomial.
15((1 + -1X)(6 + X)) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 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 + -1X = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1X = 0 + -1
-1X = 0 + -1

Combine like terms: 0 + -1 = -1
-1X = -1

Divide each side by '-1'.
X = 1

Simplifying
X = 1
Subproblem 2
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
Solution
X = {1, -6}