80r^3+52r^2-60r=0

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Solution for 80r^3+52r^2-60r=0 equation:


Simplifying
80r3 + 52r2 + -60r = 0

Reorder the terms:
-60r + 52r2 + 80r3 = 0

Solving
-60r + 52r2 + 80r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4r'.
4r(-15 + 13r + 20r2) = 0

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

Ignore the factor 4.

Subproblem 1

Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0

Subproblem 2

Set the factor '(-5 + -4r)' equal to zero and attempt to solve: Simplifying -5 + -4r = 0 Solving -5 + -4r = 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 + -4r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4r = 0 + 5 -4r = 0 + 5 Combine like terms: 0 + 5 = 5 -4r = 5 Divide each side by '-4'. r = -1.25 Simplifying r = -1.25

Subproblem 3

Set the factor '(3 + -5r)' equal to zero and attempt to solve: Simplifying 3 + -5r = 0 Solving 3 + -5r = 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 + -5r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5r = 0 + -3 -5r = 0 + -3 Combine like terms: 0 + -3 = -3 -5r = -3 Divide each side by '-5'. r = 0.6 Simplifying r = 0.6

Solution

r = {0, -1.25, 0.6}

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