-x^2-10x+150=x^2+20x-50

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Solution for -x^2-10x+150=x^2+20x-50 equation:


Simplifying
-1x2 + -10x + 150 = x2 + 20x + -50

Reorder the terms:
150 + -10x + -1x2 = x2 + 20x + -50

Reorder the terms:
150 + -10x + -1x2 = -50 + 20x + x2

Solving
150 + -10x + -1x2 = -50 + 20x + x2

Solving for variable 'x'.

Reorder the terms:
150 + 50 + -10x + -20x + -1x2 + -1x2 = -50 + 20x + x2 + 50 + -20x + -1x2

Combine like terms: 150 + 50 = 200
200 + -10x + -20x + -1x2 + -1x2 = -50 + 20x + x2 + 50 + -20x + -1x2

Combine like terms: -10x + -20x = -30x
200 + -30x + -1x2 + -1x2 = -50 + 20x + x2 + 50 + -20x + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
200 + -30x + -2x2 = -50 + 20x + x2 + 50 + -20x + -1x2

Reorder the terms:
200 + -30x + -2x2 = -50 + 50 + 20x + -20x + x2 + -1x2

Combine like terms: -50 + 50 = 0
200 + -30x + -2x2 = 0 + 20x + -20x + x2 + -1x2
200 + -30x + -2x2 = 20x + -20x + x2 + -1x2

Combine like terms: 20x + -20x = 0
200 + -30x + -2x2 = 0 + x2 + -1x2
200 + -30x + -2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
200 + -30x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(100 + -15x + -1x2) = 0

Factor a trinomial.
2((5 + -1x)(20 + x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Subproblem 2

Set the factor '(20 + x)' equal to zero and attempt to solve: Simplifying 20 + x = 0 Solving 20 + x = 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 + x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + x = 0 + -20 x = 0 + -20 Combine like terms: 0 + -20 = -20 x = -20 Simplifying x = -20

Solution

x = {5, -20}

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