5r(7r-2)(5r-3)=0

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Solution for 5r(7r-2)(5r-3)=0 equation:


Simplifying
5r(7r + -2)(5r + -3) = 0

Reorder the terms:
5r(-2 + 7r)(5r + -3) = 0

Reorder the terms:
5r(-2 + 7r)(-3 + 5r) = 0

Multiply (-2 + 7r) * (-3 + 5r)
5r(-2(-3 + 5r) + 7r * (-3 + 5r)) = 0
5r((-3 * -2 + 5r * -2) + 7r * (-3 + 5r)) = 0
5r((6 + -10r) + 7r * (-3 + 5r)) = 0
5r(6 + -10r + (-3 * 7r + 5r * 7r)) = 0
5r(6 + -10r + (-21r + 35r2)) = 0

Combine like terms: -10r + -21r = -31r
5r(6 + -31r + 35r2) = 0
(6 * 5r + -31r * 5r + 35r2 * 5r) = 0
(30r + -155r2 + 175r3) = 0

Solving
30r + -155r2 + 175r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r'.
5r(6 + -31r + 35r2) = 0

Factor a trinomial.
5r((2 + -7r)(3 + -5r)) = 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 '(2 + -7r)' equal to zero and attempt to solve: Simplifying 2 + -7r = 0 Solving 2 + -7r = 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 + -7r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7r = 0 + -2 -7r = 0 + -2 Combine like terms: 0 + -2 = -2 -7r = -2 Divide each side by '-7'. r = 0.2857142857 Simplifying r = 0.2857142857

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, 0.2857142857, 0.6}

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