3t^2=10t+8

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Solution for 3t^2=10t+8 equation:


Simplifying
3t2 = 10t + 8

Reorder the terms:
3t2 = 8 + 10t

Solving
3t2 = 8 + 10t

Solving for variable 't'.

Reorder the terms:
-8 + -10t + 3t2 = 8 + 10t + -8 + -10t

Reorder the terms:
-8 + -10t + 3t2 = 8 + -8 + 10t + -10t

Combine like terms: 8 + -8 = 0
-8 + -10t + 3t2 = 0 + 10t + -10t
-8 + -10t + 3t2 = 10t + -10t

Combine like terms: 10t + -10t = 0
-8 + -10t + 3t2 = 0

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

Subproblem 1

Set the factor '(-2 + -3t)' equal to zero and attempt to solve: Simplifying -2 + -3t = 0 Solving -2 + -3t = 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 + -3t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3t = 0 + 2 -3t = 0 + 2 Combine like terms: 0 + 2 = 2 -3t = 2 Divide each side by '-3'. t = -0.6666666667 Simplifying t = -0.6666666667

Subproblem 2

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 = {-0.6666666667, 4}

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