(8r+5)(3r-9)=0

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Solution for (8r+5)(3r-9)=0 equation:


Simplifying
(8r + 5)(3r + -9) = 0

Reorder the terms:
(5 + 8r)(3r + -9) = 0

Reorder the terms:
(5 + 8r)(-9 + 3r) = 0

Multiply (5 + 8r) * (-9 + 3r)
(5(-9 + 3r) + 8r * (-9 + 3r)) = 0
((-9 * 5 + 3r * 5) + 8r * (-9 + 3r)) = 0
((-45 + 15r) + 8r * (-9 + 3r)) = 0
(-45 + 15r + (-9 * 8r + 3r * 8r)) = 0
(-45 + 15r + (-72r + 24r2)) = 0

Combine like terms: 15r + -72r = -57r
(-45 + -57r + 24r2) = 0

Solving
-45 + -57r + 24r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -19r + 8r2) = 0

Factor a trinomial.
3((-5 + -8r)(3 + -1r)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-5 + -8r)' equal to zero and attempt to solve: Simplifying -5 + -8r = 0 Solving -5 + -8r = 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 + -8r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8r = 0 + 5 -8r = 0 + 5 Combine like terms: 0 + 5 = 5 -8r = 5 Divide each side by '-8'. r = -0.625 Simplifying r = -0.625

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 = {-0.625, 3}

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