2t^3-3t^2=20t

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Solution for 2t^3-3t^2=20t equation:


Simplifying
2t3 + -3t2 = 20t

Reorder the terms:
-3t2 + 2t3 = 20t

Solving
-3t2 + 2t3 = 20t

Solving for variable 't'.

Reorder the terms:
-20t + -3t2 + 2t3 = 20t + -20t

Combine like terms: 20t + -20t = 0
-20t + -3t2 + 2t3 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-20 + -3t + 2t2) = 0

Factor a trinomial.
t((-5 + -2t)(4 + -1t)) = 0

Subproblem 1

Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0

Subproblem 2

Set the factor '(-5 + -2t)' equal to zero and attempt to solve: Simplifying -5 + -2t = 0 Solving -5 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2t = 0 + 5 -2t = 0 + 5 Combine like terms: 0 + 5 = 5 -2t = 5 Divide each side by '-2'. t = -2.5 Simplifying t = -2.5

Subproblem 3

Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4

Solution

t = {0, -2.5, 4}

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