x(x+13)-10(x+4)=0

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Solution for x(x+13)-10(x+4)=0 equation: 


Simplifying
x(x + 13) + -10(x + 4) = 0

Reorder the terms:
x(13 + x) + -10(x + 4) = 0
(13 * x + x * x) + -10(x + 4) = 0
(13x + x2) + -10(x + 4) = 0

Reorder the terms:
13x + x2 + -10(4 + x) = 0
13x + x2 + (4 * -10 + x * -10) = 0
13x + x2 + (-40 + -10x) = 0

Reorder the terms:
-40 + 13x + -10x + x2 = 0

Combine like terms: 13x + -10x = 3x
-40 + 3x + x2 = 0

Solving
-40 + 3x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 2
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
Solution
x = {-8, 5}

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