54t^2-9t-30=0

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Solution for 54t^2-9t-30=0 equation:


Simplifying
54t2 + -9t + -30 = 0

Reorder the terms:
-30 + -9t + 54t2 = 0

Solving
-30 + -9t + 54t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -3t + 18t2) = 0

Factor a trinomial.
3((-2 + -3t)(5 + -6t)) = 0

Ignore the factor 3.

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 '(5 + -6t)' equal to zero and attempt to solve: Simplifying 5 + -6t = 0 Solving 5 + -6t = 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 + -6t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6t = 0 + -5 -6t = 0 + -5 Combine like terms: 0 + -5 = -5 -6t = -5 Divide each side by '-6'. t = 0.8333333333 Simplifying t = 0.8333333333

Solution

t = {-0.6666666667, 0.8333333333}

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