2(10-x)(x+6)=-450

Solution for 2(10-x)(x+6)=-450 equation:

Simplifying
2(10 + -1x)(x + 6) = -450

Reorder the terms:
2(10 + -1x)(6 + x) = -450

Multiply (10 + -1x) * (6 + x)
2(10(6 + x) + -1x * (6 + x)) = -450
2((6 * 10 + x * 10) + -1x * (6 + x)) = -450
2((60 + 10x) + -1x * (6 + x)) = -450
2(60 + 10x + (6 * -1x + x * -1x)) = -450
2(60 + 10x + (-6x + -1x2)) = -450

Combine like terms: 10x + -6x = 4x
2(60 + 4x + -1x2) = -450
(60 * 2 + 4x * 2 + -1x2 * 2) = -450
(120 + 8x + -2x2) = -450

Solving
120 + 8x + -2x2 = -450

Solving for variable 'x'.

Reorder the terms:
120 + 450 + 8x + -2x2 = -450 + 450

Combine like terms: 120 + 450 = 570
570 + 8x + -2x2 = -450 + 450

Combine like terms: -450 + 450 = 0
570 + 8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(285 + 4x + -1x2) = 0

Factor a trinomial.
2((19 + -1x)(15 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(19 + -1x)' equal to zero and attempt to solve:

Simplifying
19 + -1x = 0

Solving
19 + -1x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19
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 = {19, -15}