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

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


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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
(20 + x)(10 + x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-20, -10}

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