2x^2+10x+100=25-x^2-20x

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Solution for 2x^2+10x+100=25-x^2-20x equation: 


Simplifying
2x2 + 10x + 100 = 25 + -1x2 + -20x

Reorder the terms:
100 + 10x + 2x2 = 25 + -1x2 + -20x

Reorder the terms:
100 + 10x + 2x2 = 25 + -20x + -1x2

Solving
100 + 10x + 2x2 = 25 + -20x + -1x2

Solving for variable 'x'.

Reorder the terms:
100 + -25 + 10x + 20x + 2x2 + x2 = 25 + -20x + -1x2 + -25 + 20x + x2

Combine like terms: 100 + -25 = 75
75 + 10x + 20x + 2x2 + x2 = 25 + -20x + -1x2 + -25 + 20x + x2

Combine like terms: 10x + 20x = 30x
75 + 30x + 2x2 + x2 = 25 + -20x + -1x2 + -25 + 20x + x2

Combine like terms: 2x2 + x2 = 3x2
75 + 30x + 3x2 = 25 + -20x + -1x2 + -25 + 20x + x2

Reorder the terms:
75 + 30x + 3x2 = 25 + -25 + -20x + 20x + -1x2 + x2

Combine like terms: 25 + -25 = 0
75 + 30x + 3x2 = 0 + -20x + 20x + -1x2 + x2
75 + 30x + 3x2 = -20x + 20x + -1x2 + x2

Combine like terms: -20x + 20x = 0
75 + 30x + 3x2 = 0 + -1x2 + x2
75 + 30x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
75 + 30x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + 10x + x2) = 0

Factor a trinomial.
3((5 + x)(5 + x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-5, -5}

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