-4(4t^2-24t+27)=0

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Solution for -4(4t^2-24t+27)=0 equation:


Simplifying
-4(4t2 + -24t + 27) = 0

Reorder the terms:
-4(27 + -24t + 4t2) = 0
(27 * -4 + -24t * -4 + 4t2 * -4) = 0
(-108 + 96t + -16t2) = 0

Solving
-108 + 96t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-27 + 24t + -4t2) = 0

Factor a trinomial.
4((-9 + 2t)(3 + -2t)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-9 + 2t)' equal to zero and attempt to solve: Simplifying -9 + 2t = 0 Solving -9 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2t = 0 + 9 2t = 0 + 9 Combine like terms: 0 + 9 = 9 2t = 9 Divide each side by '2'. t = 4.5 Simplifying t = 4.5

Subproblem 2

Set the factor '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5

Solution

t = {4.5, 1.5}

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