25=20t+5t^2

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


Simplifying
25 = 20t + 5t2

Solving
25 = 20t + 5t2

Solving for variable 't'.

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

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

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

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + -4t + -1t2) = 0

Factor a trinomial.
5((1 + -1t)(5 + t)) = 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 + 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 = {1, -5}

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