25=-5t^2+30t

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Solution for 25=-5t^2+30t equation:


Simplifying
25 = -5t2 + 30t

Reorder the terms:
25 = 30t + -5t2

Solving
25 = 30t + -5t2

Solving for variable 't'.

Reorder the terms:
25 + -30t + 5t2 = 30t + -30t + -5t2 + 5t2

Combine like terms: 30t + -30t = 0
25 + -30t + 5t2 = 0 + -5t2 + 5t2
25 + -30t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
25 + -30t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + -6t + t2) = 0

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

Solution

t = {1, 5}

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