(12t+7)(5t-2)=0

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Solution for (12t+7)(5t-2)=0 equation:


Simplifying
(12t + 7)(5t + -2) = 0

Reorder the terms:
(7 + 12t)(5t + -2) = 0

Reorder the terms:
(7 + 12t)(-2 + 5t) = 0

Multiply (7 + 12t) * (-2 + 5t)
(7(-2 + 5t) + 12t * (-2 + 5t)) = 0
((-2 * 7 + 5t * 7) + 12t * (-2 + 5t)) = 0
((-14 + 35t) + 12t * (-2 + 5t)) = 0
(-14 + 35t + (-2 * 12t + 5t * 12t)) = 0
(-14 + 35t + (-24t + 60t2)) = 0

Combine like terms: 35t + -24t = 11t
(-14 + 11t + 60t2) = 0

Solving
-14 + 11t + 60t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-7 + -12t)(2 + -5t) = 0

Subproblem 1

Set the factor '(-7 + -12t)' equal to zero and attempt to solve: Simplifying -7 + -12t = 0 Solving -7 + -12t = 0 Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -12t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -12t = 0 + 7 -12t = 0 + 7 Combine like terms: 0 + 7 = 7 -12t = 7 Divide each side by '-12'. t = -0.5833333333 Simplifying t = -0.5833333333

Subproblem 2

Set the factor '(2 + -5t)' equal to zero and attempt to solve: Simplifying 2 + -5t = 0 Solving 2 + -5t = 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 + -5t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5t = 0 + -2 -5t = 0 + -2 Combine like terms: 0 + -2 = -2 -5t = -2 Divide each side by '-5'. t = 0.4 Simplifying t = 0.4

Solution

t = {-0.5833333333, 0.4}

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