(3r-6)(5r+4)=

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Solution for (3r-6)(5r+4)= equation:


Simplifying
(3r + -6)(5r + 4) = 0

Reorder the terms:
(-6 + 3r)(5r + 4) = 0

Reorder the terms:
(-6 + 3r)(4 + 5r) = 0

Multiply (-6 + 3r) * (4 + 5r)
(-6(4 + 5r) + 3r * (4 + 5r)) = 0
((4 * -6 + 5r * -6) + 3r * (4 + 5r)) = 0
((-24 + -30r) + 3r * (4 + 5r)) = 0
(-24 + -30r + (4 * 3r + 5r * 3r)) = 0
(-24 + -30r + (12r + 15r2)) = 0

Combine like terms: -30r + 12r = -18r
(-24 + -18r + 15r2) = 0

Solving
-24 + -18r + 15r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -6r + 5r2) = 0

Factor a trinomial.
3((-4 + -5r)(2 + -1r)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-4 + -5r)' equal to zero and attempt to solve: Simplifying -4 + -5r = 0 Solving -4 + -5r = 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 + -5r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5r = 0 + 4 -5r = 0 + 4 Combine like terms: 0 + 4 = 4 -5r = 4 Divide each side by '-5'. r = -0.8 Simplifying r = -0.8

Subproblem 2

Set the factor '(2 + -1r)' equal to zero and attempt to solve: Simplifying 2 + -1r = 0 Solving 2 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1r = 0 + -2 -1r = 0 + -2 Combine like terms: 0 + -2 = -2 -1r = -2 Divide each side by '-1'. r = 2 Simplifying r = 2

Solution

r = {-0.8, 2}

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