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

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


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

Reorder the terms:
(-5 + 4t)(t + 8) = 0

Reorder the terms:
(-5 + 4t)(8 + t) = 0

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

Combine like terms: -5t + 32t = 27t
(-40 + 27t + 4t2) = 0

Solving
-40 + 27t + 4t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-8 + -1t)(5 + -4t) = 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 + -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 = {-8, 1.25}

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