90x-10x^2=180

Solution for 90x-10x^2=180 equation:

Simplifying
90x + -10x2 = 180

Solving
90x + -10x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 90x + -10x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 90x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-18 + 9x + -1x2) = 0

Factor a trinomial.
10((-6 + x)(3 + -1x)) = 0

Ignore the factor 10.
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 '(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
Solution
x = {6, 3}