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

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


Simplifying
x2 + -2x + 25 = -10x + 10

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

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

Solving
25 + -2x + x2 = 10 + -10x

Solving for variable 'x'.

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

Combine like terms: 25 + -10 = 15
15 + -2x + 10x + x2 = 10 + -10x + -10 + 10x

Combine like terms: -2x + 10x = 8x
15 + 8x + x2 = 10 + -10x + -10 + 10x

Reorder the terms:
15 + 8x + x2 = 10 + -10 + -10x + 10x

Combine like terms: 10 + -10 = 0
15 + 8x + x2 = 0 + -10x + 10x
15 + 8x + x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
15 + 8x + x2 = 0

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


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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-5, -3}

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