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

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


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

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

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

Multiply (5 + 7t) * (-5 + 2t)
(5(-5 + 2t) + 7t * (-5 + 2t)) = 0
((-5 * 5 + 2t * 5) + 7t * (-5 + 2t)) = 0
((-25 + 10t) + 7t * (-5 + 2t)) = 0
(-25 + 10t + (-5 * 7t + 2t * 7t)) = 0
(-25 + 10t + (-35t + 14t2)) = 0

Combine like terms: 10t + -35t = -25t
(-25 + -25t + 14t2) = 0

Solving
-25 + -25t + 14t2 = 0

Solving for variable 't'.

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

Subproblem 1

Set the factor '(-5 + -7t)' equal to zero and attempt to solve: Simplifying -5 + -7t = 0 Solving -5 + -7t = 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 + -7t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7t = 0 + 5 -7t = 0 + 5 Combine like terms: 0 + 5 = 5 -7t = 5 Divide each side by '-7'. t = -0.7142857143 Simplifying t = -0.7142857143

Subproblem 2

Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 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 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5

Solution

t = {-0.7142857143, 2.5}

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