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

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


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

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

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

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

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

Reorder the terms:
-5 + 4x + x2 = (-5 + -1x)(2x + 3)

Reorder the terms:
-5 + 4x + x2 = (-5 + -1x)(3 + 2x)

Multiply (-5 + -1x) * (3 + 2x)
-5 + 4x + x2 = (-5(3 + 2x) + -1x * (3 + 2x))
-5 + 4x + x2 = ((3 * -5 + 2x * -5) + -1x * (3 + 2x))
-5 + 4x + x2 = ((-15 + -10x) + -1x * (3 + 2x))
-5 + 4x + x2 = (-15 + -10x + (3 * -1x + 2x * -1x))
-5 + 4x + x2 = (-15 + -10x + (-3x + -2x2))

Combine like terms: -10x + -3x = -13x
-5 + 4x + x2 = (-15 + -13x + -2x2)

Solving
-5 + 4x + x2 = -15 + -13x + -2x2

Solving for variable 'x'.

Reorder the terms:
-5 + 15 + 4x + 13x + x2 + 2x2 = -15 + -13x + -2x2 + 15 + 13x + 2x2

Combine like terms: -5 + 15 = 10
10 + 4x + 13x + x2 + 2x2 = -15 + -13x + -2x2 + 15 + 13x + 2x2

Combine like terms: 4x + 13x = 17x
10 + 17x + x2 + 2x2 = -15 + -13x + -2x2 + 15 + 13x + 2x2

Combine like terms: x2 + 2x2 = 3x2
10 + 17x + 3x2 = -15 + -13x + -2x2 + 15 + 13x + 2x2

Reorder the terms:
10 + 17x + 3x2 = -15 + 15 + -13x + 13x + -2x2 + 2x2

Combine like terms: -15 + 15 = 0
10 + 17x + 3x2 = 0 + -13x + 13x + -2x2 + 2x2
10 + 17x + 3x2 = -13x + 13x + -2x2 + 2x2

Combine like terms: -13x + 13x = 0
10 + 17x + 3x2 = 0 + -2x2 + 2x2
10 + 17x + 3x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
10 + 17x + 3x2 = 0

Factor a trinomial.
(5 + x)(2 + 3x) = 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 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-5, -0.6666666667}

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