-6x^2=-96x+360

Solution for -6x^2=-96x+360 equation:

Simplifying
-6x2 = -96x + 360

Reorder the terms:
-6x2 = 360 + -96x

Solving
-6x2 = 360 + -96x

Solving for variable 'x'.

Reorder the terms:
-360 + 96x + -6x2 = 360 + -96x + -360 + 96x

Reorder the terms:
-360 + 96x + -6x2 = 360 + -360 + -96x + 96x

Combine like terms: 360 + -360 = 0
-360 + 96x + -6x2 = 0 + -96x + 96x
-360 + 96x + -6x2 = -96x + 96x

Combine like terms: -96x + 96x = 0
-360 + 96x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-60 + 16x + -1x2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

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

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10
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 = {10, 6}