5r(8r-5)(5r-1)=0

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Solution for 5r(8r-5)(5r-1)=0 equation:


Simplifying
5r(8r + -5)(5r + -1) = 0

Reorder the terms:
5r(-5 + 8r)(5r + -1) = 0

Reorder the terms:
5r(-5 + 8r)(-1 + 5r) = 0

Multiply (-5 + 8r) * (-1 + 5r)
5r(-5(-1 + 5r) + 8r * (-1 + 5r)) = 0
5r((-1 * -5 + 5r * -5) + 8r * (-1 + 5r)) = 0
5r((5 + -25r) + 8r * (-1 + 5r)) = 0
5r(5 + -25r + (-1 * 8r + 5r * 8r)) = 0
5r(5 + -25r + (-8r + 40r2)) = 0

Combine like terms: -25r + -8r = -33r
5r(5 + -33r + 40r2) = 0
(5 * 5r + -33r * 5r + 40r2 * 5r) = 0
(25r + -165r2 + 200r3) = 0

Solving
25r + -165r2 + 200r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r'.
5r(5 + -33r + 40r2) = 0

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

Ignore the factor 5.

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 '(1 + -5r)' equal to zero and attempt to solve: Simplifying 1 + -5r = 0 Solving 1 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5r = 0 + -1 -5r = 0 + -1 Combine like terms: 0 + -1 = -1 -5r = -1 Divide each side by '-5'. r = 0.2 Simplifying r = 0.2

Subproblem 3

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

Solution

r = {0, 0.2, 0.625}

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