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

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


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

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

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

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

Combine like terms: 3t + -8t = -5t
5(-24 + -5t + t2) = 0
(-24 * 5 + -5t * 5 + t2 * 5) = 0
(-120 + -25t + 5t2) = 0

Solving
-120 + -25t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-24 + -5t + t2) = 0

Factor a trinomial.
5((-3 + -1t)(8 + -1t)) = 0

Ignore the factor 5.

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

Simplifying
-3 + -1t = 0

Solving
-3 + -1t = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1t = 0 + 3
-1t = 0 + 3

Combine like terms: 0 + 3 = 3
-1t = 3

Divide each side by '-1'.
t = -3

Simplifying
t = -3

Subproblem 2
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
Solution
t = {-3, 8}

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