(x-1)(x+5)=-8

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Solution for (x-1)(x+5)=-8 equation:


Simplifying
(x + -1)(x + 5) = -8

Reorder the terms:
(-1 + x)(x + 5) = -8

Reorder the terms:
(-1 + x)(5 + x) = -8

Multiply (-1 + x) * (5 + x)
(-1(5 + x) + x(5 + x)) = -8
((5 * -1 + x * -1) + x(5 + x)) = -8
((-5 + -1x) + x(5 + x)) = -8
(-5 + -1x + (5 * x + x * x)) = -8
(-5 + -1x + (5x + x2)) = -8

Combine like terms: -1x + 5x = 4x
(-5 + 4x + x2) = -8

Solving
-5 + 4x + x2 = -8

Solving for variable 'x'.

Reorder the terms:
-5 + 8 + 4x + x2 = -8 + 8

Combine like terms: -5 + 8 = 3
3 + 4x + x2 = -8 + 8

Combine like terms: -8 + 8 = 0
3 + 4x + x2 = 0

Factor a trinomial.
(3 + x)(1 + x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-3, -1}

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