5t^2+10t-15=0

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Solution for 5t^2+10t-15=0 equation:


Simplifying
5t2 + 10t + -15 = 0

Reorder the terms:
-15 + 10t + 5t2 = 0

Solving
-15 + 10t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + 2t + t2) = 0

Factor a trinomial.
5((-3 + -1t)(1 + -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 '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1

Solution

t = {-3, 1}

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