(r-3)(r+6)=0

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Solution for (r-3)(r+6)=0 equation:


Simplifying
(r + -3)(r + 6) = 0

Reorder the terms:
(-3 + r)(r + 6) = 0

Reorder the terms:
(-3 + r)(6 + r) = 0

Multiply (-3 + r) * (6 + r)
(-3(6 + r) + r(6 + r)) = 0
((6 * -3 + r * -3) + r(6 + r)) = 0
((-18 + -3r) + r(6 + r)) = 0
(-18 + -3r + (6 * r + r * r)) = 0
(-18 + -3r + (6r + r2)) = 0

Combine like terms: -3r + 6r = 3r
(-18 + 3r + r2) = 0

Solving
-18 + 3r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-6 + -1r)(3 + -1r) = 0

Subproblem 1

Set the factor '(-6 + -1r)' equal to zero and attempt to solve: Simplifying -6 + -1r = 0 Solving -6 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1r = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1r = 0 + 6 -1r = 0 + 6 Combine like terms: 0 + 6 = 6 -1r = 6 Divide each side by '-1'. r = -6 Simplifying r = -6

Subproblem 2

Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3

Solution

r = {-6, 3}

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