(5+4t)(8-5t)=0

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Solution for (5+4t)(8-5t)=0 equation: 


Simplifying
(5 + 4t)(8 + -5t) = 0

Multiply (5 + 4t) * (8 + -5t)
(5(8 + -5t) + 4t * (8 + -5t)) = 0
((8 * 5 + -5t * 5) + 4t * (8 + -5t)) = 0
((40 + -25t) + 4t * (8 + -5t)) = 0
(40 + -25t + (8 * 4t + -5t * 4t)) = 0
(40 + -25t + (32t + -20t2)) = 0

Combine like terms: -25t + 32t = 7t
(40 + 7t + -20t2) = 0

Solving
40 + 7t + -20t2 = 0

Solving for variable 't'.

Factor a trinomial.
(8 + -5t)(5 + 4t) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + 4t)' equal to zero and attempt to solve:

Simplifying
5 + 4t = 0

Solving
5 + 4t = 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 + 4t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4t = 0 + -5
4t = 0 + -5

Combine like terms: 0 + -5 = -5
4t = -5

Divide each side by '4'.
t = -1.25

Simplifying
t = -1.25
Solution
t = {1.6, -1.25}

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