-5t^2-10t+75=0

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Solution for -5t^2-10t+75=0 equation:


Simplifying
-5t2 + -10t + 75 = 0

Reorder the terms:
75 + -10t + -5t2 = 0

Solving
75 + -10t + -5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(15 + -2t + -1t2) = 0

Factor a trinomial.
5((3 + -1t)(5 + t)) = 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 '(5 + t)' equal to zero and attempt to solve: Simplifying 5 + t = 0 Solving 5 + t = 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 + t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + t = 0 + -5 t = 0 + -5 Combine like terms: 0 + -5 = -5 t = -5 Simplifying t = -5

Solution

t = {3, -5}

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