4t^4+18t^3-10t^2=0

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Solution for 4t^4+18t^3-10t^2=0 equation:


Simplifying
4t4 + 18t3 + -10t2 = 0

Reorder the terms:
-10t2 + 18t3 + 4t4 = 0

Solving
-10t2 + 18t3 + 4t4 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2t2'.
2t2(-5 + 9t + 2t2) = 0

Factor a trinomial.
2t2((-5 + -1t)(1 + -2t)) = 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 '(-5 + -1t)' equal to zero and attempt to solve: Simplifying -5 + -1t = 0 Solving -5 + -1t = 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 + -1t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1t = 0 + 5 -1t = 0 + 5 Combine like terms: 0 + 5 = 5 -1t = 5 Divide each side by '-1'. t = -5 Simplifying t = -5

Subproblem 3

Set the factor '(1 + -2t)' equal to zero and attempt to solve: Simplifying 1 + -2t = 0 Solving 1 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2t = 0 + -1 -2t = 0 + -1 Combine like terms: 0 + -1 = -1 -2t = -1 Divide each side by '-2'. t = 0.5 Simplifying t = 0.5

Solution

t = {0, -5, 0.5}

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