15r^3+80r^2+105r=

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Solution for 15r^3+80r^2+105r= equation:


Simplifying
15r3 + 80r2 + 105r = 0

Reorder the terms:
105r + 80r2 + 15r3 = 0

Solving
105r + 80r2 + 15r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5r'.
5r(21 + 16r + 3r2) = 0

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

Subproblem 3

Set the factor '(7 + 3r)' equal to zero and attempt to solve: Simplifying 7 + 3r = 0 Solving 7 + 3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3r = 0 + -7 3r = 0 + -7 Combine like terms: 0 + -7 = -7 3r = -7 Divide each side by '3'. r = -2.333333333 Simplifying r = -2.333333333

Solution

r = {0, -3, -2.333333333}

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