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

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


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

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

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

Multiply (-5 + 7t) * (8 + t)
(-5(8 + t) + 7t * (8 + t)) = 0
((8 * -5 + t * -5) + 7t * (8 + t)) = 0
((-40 + -5t) + 7t * (8 + t)) = 0
(-40 + -5t + (8 * 7t + t * 7t)) = 0
(-40 + -5t + (56t + 7t2)) = 0

Combine like terms: -5t + 56t = 51t
(-40 + 51t + 7t2) = 0

Solving
-40 + 51t + 7t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-8 + -1t)(5 + -7t) = 0


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

Simplifying
-8 + -1t = 0

Solving
-8 + -1t = 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 + -1t = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1t = 0 + 8
-1t = 0 + 8

Combine like terms: 0 + 8 = 8
-1t = 8

Divide each side by '-1'.
t = -8

Simplifying
t = -8

Subproblem 2
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
Solution
t = {-8, 0.7142857143}

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