6(8t+4)(3t+6)=0

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Solution for 6(8t+4)(3t+6)=0 equation:


Simplifying
6(8t + 4)(3t + 6) = 0

Reorder the terms:
6(4 + 8t)(3t + 6) = 0

Reorder the terms:
6(4 + 8t)(6 + 3t) = 0

Multiply (4 + 8t) * (6 + 3t)
6(4(6 + 3t) + 8t * (6 + 3t)) = 0
6((6 * 4 + 3t * 4) + 8t * (6 + 3t)) = 0
6((24 + 12t) + 8t * (6 + 3t)) = 0
6(24 + 12t + (6 * 8t + 3t * 8t)) = 0
6(24 + 12t + (48t + 24t2)) = 0

Combine like terms: 12t + 48t = 60t
6(24 + 60t + 24t2) = 0
(24 * 6 + 60t * 6 + 24t2 * 6) = 0
(144 + 360t + 144t2) = 0

Solving
144 + 360t + 144t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '72'.
72(2 + 5t + 2t2) = 0

Factor a trinomial.
72((2 + t)(1 + 2t)) = 0

Ignore the factor 72.

Subproblem 1

Set the factor '(2 + t)' equal to zero and attempt to solve: Simplifying 2 + t = 0 Solving 2 + t = 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 + t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + t = 0 + -2 t = 0 + -2 Combine like terms: 0 + -2 = -2 t = -2 Simplifying t = -2

Subproblem 2

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 = {-2, -0.5}

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