360x-360x+1800=6x^2-30x

Solution for 360x-360x+1800=6x^2-30x equation:

Simplifying
360x + -360x + 1800 = 6x2 + -30x

Reorder the terms:
1800 + 360x + -360x = 6x2 + -30x

Combine like terms: 360x + -360x = 0
1800 + 0 = 6x2 + -30x
1800 = 6x2 + -30x

Reorder the terms:
1800 = -30x + 6x2

Solving
1800 = -30x + 6x2

Solving for variable 'x'.

Reorder the terms:
1800 + 30x + -6x2 = -30x + 30x + 6x2 + -6x2

Combine like terms: -30x + 30x = 0
1800 + 30x + -6x2 = 0 + 6x2 + -6x2
1800 + 30x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
1800 + 30x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(300 + 5x + -1x2) = 0

Factor a trinomial.
6((20 + -1x)(15 + x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Subproblem 2
Set the factor '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 0

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

Add '-15' to each side of the equation.
15 + -15 + x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + x = 0 + -15
x = 0 + -15

Combine like terms: 0 + -15 = -15
x = -15

Simplifying
x = -15
Solution
x = {20, -15}