(5t-12)(6t+3)=0

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Solution for (5t-12)(6t+3)=0 equation:


Simplifying
(5t + -12)(6t + 3) = 0

Reorder the terms:
(-12 + 5t)(6t + 3) = 0

Reorder the terms:
(-12 + 5t)(3 + 6t) = 0

Multiply (-12 + 5t) * (3 + 6t)
(-12(3 + 6t) + 5t * (3 + 6t)) = 0
((3 * -12 + 6t * -12) + 5t * (3 + 6t)) = 0
((-36 + -72t) + 5t * (3 + 6t)) = 0
(-36 + -72t + (3 * 5t + 6t * 5t)) = 0
(-36 + -72t + (15t + 30t2)) = 0

Combine like terms: -72t + 15t = -57t
(-36 + -57t + 30t2) = 0

Solving
-36 + -57t + 30t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -19t + 10t2) = 0

Factor a trinomial.
3((-1 + -2t)(12 + -5t)) = 0

Ignore the factor 3.

Subproblem 1

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

Subproblem 2

Set the factor '(12 + -5t)' equal to zero and attempt to solve: Simplifying 12 + -5t = 0 Solving 12 + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -5t = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -5t = 0 + -12 -5t = 0 + -12 Combine like terms: 0 + -12 = -12 -5t = -12 Divide each side by '-5'. t = 2.4 Simplifying t = 2.4

Solution

t = {-0.5, 2.4}

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