2r^3=14r+3r^2

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Solution for 2r^3=14r+3r^2 equation:


Simplifying
2r3 = 14r + 3r2

Solving
2r3 = 14r + 3r2

Solving for variable 'r'.

Reorder the terms:
-14r + -3r2 + 2r3 = 14r + 3r2 + -14r + -3r2

Reorder the terms:
-14r + -3r2 + 2r3 = 14r + -14r + 3r2 + -3r2

Combine like terms: 14r + -14r = 0
-14r + -3r2 + 2r3 = 0 + 3r2 + -3r2
-14r + -3r2 + 2r3 = 3r2 + -3r2

Combine like terms: 3r2 + -3r2 = 0
-14r + -3r2 + 2r3 = 0

Factor out the Greatest Common Factor (GCF), 'r'.
r(-14 + -3r + 2r2) = 0

Factor a trinomial.
r((-2 + -1r)(7 + -2r)) = 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 '(-2 + -1r)' equal to zero and attempt to solve: Simplifying -2 + -1r = 0 Solving -2 + -1r = 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 + -1r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1r = 0 + 2 -1r = 0 + 2 Combine like terms: 0 + 2 = 2 -1r = 2 Divide each side by '-1'. r = -2 Simplifying r = -2

Subproblem 3

Set the factor '(7 + -2r)' equal to zero and attempt to solve: Simplifying 7 + -2r = 0 Solving 7 + -2r = 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 + -2r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2r = 0 + -7 -2r = 0 + -7 Combine like terms: 0 + -7 = -7 -2r = -7 Divide each side by '-2'. r = 3.5 Simplifying r = 3.5

Solution

r = {0, -2, 3.5}

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