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

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


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

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

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

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

Combine like terms: -25t + 8t = -17t
(-40 + -17t + 5t2) = 0

Solving
-40 + -17t + 5t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-8 + -5t)(5 + -1t) = 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 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 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 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-1.6, 5}

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