6t^4-20t^3+16t^2=

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Solution for 6t^4-20t^3+16t^2= equation:


Simplifying
6t4 + -20t3 + 16t2 = 0

Reorder the terms:
16t2 + -20t3 + 6t4 = 0

Solving
16t2 + -20t3 + 6t4 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2t2'.
2t2(8 + -10t + 3t2) = 0

Factor a trinomial.
2t2((4 + -3t)(2 + -1t)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 't2' equal to zero and attempt to solve: Simplifying t2 = 0 Solving t2 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t2 = 0 Take the square root of each side: t = {0}

Subproblem 2

Set the factor '(4 + -3t)' equal to zero and attempt to solve: Simplifying 4 + -3t = 0 Solving 4 + -3t = 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 + -3t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3t = 0 + -4 -3t = 0 + -4 Combine like terms: 0 + -4 = -4 -3t = -4 Divide each side by '-3'. t = 1.333333333 Simplifying t = 1.333333333

Subproblem 3

Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2

Solution

t = {0, 1.333333333, 2}

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