20=25t-5t^2

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Solution for 20=25t-5t^2 equation:


Simplifying
20 = 25t + -5t2

Solving
20 = 25t + -5t2

Solving for variable 't'.

Reorder the terms:
20 + -25t + 5t2 = 25t + -25t + -5t2 + 5t2

Combine like terms: 25t + -25t = 0
20 + -25t + 5t2 = 0 + -5t2 + 5t2
20 + -25t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
20 + -25t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + -5t + t2) = 0

Factor a trinomial.
5((1 + -1t)(4 + -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 '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4

Solution

t = {1, 4}

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