10=-5t^2+15t

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


Simplifying
10 = -5t2 + 15t

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

Solving
10 = 15t + -5t2

Solving for variable 't'.

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

Combine like terms: 15t + -15t = 0
10 + -15t + 5t2 = 0 + -5t2 + 5t2
10 + -15t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
10 + -15t + 5t2 = 0

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

Factor a trinomial.
5((1 + -1t)(2 + -1t)) = 0

Ignore the factor 5.

Subproblem 1

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

Subproblem 2

Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2

Solution

t = {1, 2}

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