2r^3+15r^2=r^4

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Solution for 2r^3+15r^2=r^4 equation:


Simplifying
2r3 + 15r2 = r4

Reorder the terms:
15r2 + 2r3 = r4

Solving
15r2 + 2r3 = r4

Solving for variable 'r'.

Combine like terms: r4 + -1r4 = 0
15r2 + 2r3 + -1r4 = 0

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(15 + 2r + -1r2) = 0

Factor a trinomial.
r2((5 + -1r)(3 + r)) = 0

Subproblem 1

Set the factor 'r2' equal to zero and attempt to solve: Simplifying r2 = 0 Solving r2 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r2 = 0 Take the square root of each side: r = {0}

Subproblem 2

Set the factor '(5 + -1r)' equal to zero and attempt to solve: Simplifying 5 + -1r = 0 Solving 5 + -1r = 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 + -1r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1r = 0 + -5 -1r = 0 + -5 Combine like terms: 0 + -5 = -5 -1r = -5 Divide each side by '-1'. r = 5 Simplifying r = 5

Subproblem 3

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

Solution

r = {0, 5, -3}

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