(x-1)(x+5)=0

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


Simplifying
(x + -1)(x + 5) = 0

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

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

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

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

Solving
-5 + 4x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Solution

x = {-5, 1}

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