3r=10r(r-2)

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Solution for 3r=10r(r-2) equation:


Simplifying
3r = 10r(r + -2)

Reorder the terms:
3r = 10r(-2 + r)
3r = (-2 * 10r + r * 10r)
3r = (-20r + 10r2)

Solving
3r = -20r + 10r2

Solving for variable 'r'.

Combine like terms: 3r + 20r = 23r
23r + -10r2 = -20r + 10r2 + 20r + -10r2

Reorder the terms:
23r + -10r2 = -20r + 20r + 10r2 + -10r2

Combine like terms: -20r + 20r = 0
23r + -10r2 = 0 + 10r2 + -10r2
23r + -10r2 = 10r2 + -10r2

Combine like terms: 10r2 + -10r2 = 0
23r + -10r2 = 0

Factor out the Greatest Common Factor (GCF), 'r'.
r(23 + -10r) = 0

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 '(23 + -10r)' equal to zero and attempt to solve: Simplifying 23 + -10r = 0 Solving 23 + -10r = 0 Move all terms containing r to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + -10r = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -10r = 0 + -23 -10r = 0 + -23 Combine like terms: 0 + -23 = -23 -10r = -23 Divide each side by '-10'. r = 2.3 Simplifying r = 2.3

Solution

r = {0, 2.3}

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