(r-4)(2r+6)=0

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Solution for (r-4)(2r+6)=0 equation:


Simplifying
(r + -4)(2r + 6) = 0

Reorder the terms:
(-4 + r)(2r + 6) = 0

Reorder the terms:
(-4 + r)(6 + 2r) = 0

Multiply (-4 + r) * (6 + 2r)
(-4(6 + 2r) + r(6 + 2r)) = 0
((6 * -4 + 2r * -4) + r(6 + 2r)) = 0
((-24 + -8r) + r(6 + 2r)) = 0
(-24 + -8r + (6 * r + 2r * r)) = 0
(-24 + -8r + (6r + 2r2)) = 0

Combine like terms: -8r + 6r = -2r
(-24 + -2r + 2r2) = 0

Solving
-24 + -2r + 2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -1r + r2) = 0

Factor a trinomial.
2((-3 + -1r)(4 + -1r)) = 0

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(4 + -1r)' equal to zero and attempt to solve: Simplifying 4 + -1r = 0 Solving 4 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1r = 0 + -4 -1r = 0 + -4 Combine like terms: 0 + -4 = -4 -1r = -4 Divide each side by '-1'. r = 4 Simplifying r = 4

Solution

r = {-3, 4}

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