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

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


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

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

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

Multiply (8 + 5t) * (5 + -3t)
(8(5 + -3t) + 5t * (5 + -3t)) = 0
((5 * 8 + -3t * 8) + 5t * (5 + -3t)) = 0
((40 + -24t) + 5t * (5 + -3t)) = 0
(40 + -24t + (5 * 5t + -3t * 5t)) = 0
(40 + -24t + (25t + -15t2)) = 0

Combine like terms: -24t + 25t = 1t
(40 + 1t + -15t2) = 0

Solving
40 + 1t + -15t2 = 0

Solving for variable 't'.

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


Subproblem 1
Set the factor '(5 + -3t)' equal to zero and attempt to solve:

Simplifying
5 + -3t = 0

Solving
5 + -3t = 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 + -3t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3t = 0 + -5
-3t = 0 + -5

Combine like terms: 0 + -5 = -5
-3t = -5

Divide each side by '-3'.
t = 1.666666667

Simplifying
t = 1.666666667

Subproblem 2
Set the factor '(8 + 5t)' equal to zero and attempt to solve:

Simplifying
8 + 5t = 0

Solving
8 + 5t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + 5t = 0 + -8

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

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

Divide each side by '5'.
t = -1.6

Simplifying
t = -1.6
Solution
t = {1.666666667, -1.6}

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