(8t+5)(3t-7)=0

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Solution for (8t+5)(3t-7)=0 equation: 


Simplifying
(8t + 5)(3t + -7) = 0

Reorder the terms:
(5 + 8t)(3t + -7) = 0

Reorder the terms:
(5 + 8t)(-7 + 3t) = 0

Multiply (5 + 8t) * (-7 + 3t)
(5(-7 + 3t) + 8t * (-7 + 3t)) = 0
((-7 * 5 + 3t * 5) + 8t * (-7 + 3t)) = 0
((-35 + 15t) + 8t * (-7 + 3t)) = 0
(-35 + 15t + (-7 * 8t + 3t * 8t)) = 0
(-35 + 15t + (-56t + 24t2)) = 0

Combine like terms: 15t + -56t = -41t
(-35 + -41t + 24t2) = 0

Solving
-35 + -41t + 24t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-5 + -8t)(7 + -3t) = 0


Subproblem 1
Set the factor '(-5 + -8t)' equal to zero and attempt to solve:

Simplifying
-5 + -8t = 0

Solving
-5 + -8t = 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 + -8t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -8t = 0 + 5
-8t = 0 + 5

Combine like terms: 0 + 5 = 5
-8t = 5

Divide each side by '-8'.
t = -0.625

Simplifying
t = -0.625

Subproblem 2
Set the factor '(7 + -3t)' equal to zero and attempt to solve:

Simplifying
7 + -3t = 0

Solving
7 + -3t = 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 + -3t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3t = 0 + -7
-3t = 0 + -7

Combine like terms: 0 + -7 = -7
-3t = -7

Divide each side by '-3'.
t = 2.333333333

Simplifying
t = 2.333333333
Solution
t = {-0.625, 2.333333333}

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