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

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


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

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

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

Multiply (5 + r) * (-1 + r)
(5(-1 + r) + r(-1 + r)) = 0
((-1 * 5 + r * 5) + r(-1 + r)) = 0
((-5 + 5r) + r(-1 + r)) = 0
(-5 + 5r + (-1 * r + r * r)) = 0
(-5 + 5r + (-1r + r2)) = 0

Combine like terms: 5r + -1r = 4r
(-5 + 4r + r2) = 0

Solving
-5 + 4r + r2 = 0

Solving for variable 'r'.

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

Subproblem 1

Set the factor '(-5 + -1r)' equal to zero and attempt to solve: Simplifying -5 + -1r = 0 Solving -5 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1r = 0 + 5 -1r = 0 + 5 Combine like terms: 0 + 5 = 5 -1r = 5 Divide each side by '-1'. r = -5 Simplifying r = -5

Subproblem 2

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

Solution

r = {-5, 1}

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