(x-5)(x+1)-2x(x-3)+13=0

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Solution for (x-5)(x+1)-2x(x-3)+13=0 equation: 


Simplifying
(x + -5)(x + 1) + -2x(x + -3) + 13 = 0

Reorder the terms:
(-5 + x)(x + 1) + -2x(x + -3) + 13 = 0

Reorder the terms:
(-5 + x)(1 + x) + -2x(x + -3) + 13 = 0

Multiply (-5 + x) * (1 + x)
(-5(1 + x) + x(1 + x)) + -2x(x + -3) + 13 = 0
((1 * -5 + x * -5) + x(1 + x)) + -2x(x + -3) + 13 = 0
((-5 + -5x) + x(1 + x)) + -2x(x + -3) + 13 = 0
(-5 + -5x + (1 * x + x * x)) + -2x(x + -3) + 13 = 0
(-5 + -5x + (1x + x2)) + -2x(x + -3) + 13 = 0

Combine like terms: -5x + 1x = -4x
(-5 + -4x + x2) + -2x(x + -3) + 13 = 0

Reorder the terms:
-5 + -4x + x2 + -2x(-3 + x) + 13 = 0
-5 + -4x + x2 + (-3 * -2x + x * -2x) + 13 = 0
-5 + -4x + x2 + (6x + -2x2) + 13 = 0

Reorder the terms:
-5 + 13 + -4x + 6x + x2 + -2x2 = 0

Combine like terms: -5 + 13 = 8
8 + -4x + 6x + x2 + -2x2 = 0

Combine like terms: -4x + 6x = 2x
8 + 2x + x2 + -2x2 = 0

Combine like terms: x2 + -2x2 = -1x2
8 + 2x + -1x2 = 0

Solving
8 + 2x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(2 + x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {4, -2}

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