x^2+13x=6x-10

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Solution for x^2+13x=6x-10 equation: 


Simplifying
x2 + 13x = 6x + -10

Reorder the terms:
13x + x2 = 6x + -10

Reorder the terms:
13x + x2 = -10 + 6x

Solving
13x + x2 = -10 + 6x

Solving for variable 'x'.

Reorder the terms:
10 + 13x + -6x + x2 = -10 + 6x + 10 + -6x

Combine like terms: 13x + -6x = 7x
10 + 7x + x2 = -10 + 6x + 10 + -6x

Reorder the terms:
10 + 7x + x2 = -10 + 10 + 6x + -6x

Combine like terms: -10 + 10 = 0
10 + 7x + x2 = 0 + 6x + -6x
10 + 7x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
10 + 7x + x2 = 0

Factor a trinomial.
(5 + x)(2 + 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-5, -2}

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