205=-5t^2+60t+25

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Solution for 205=-5t^2+60t+25 equation:


Simplifying
205 = -5t2 + 60t + 25

Reorder the terms:
205 = 25 + 60t + -5t2

Solving
205 = 25 + 60t + -5t2

Solving for variable 't'.

Combine like terms: 205 + -25 = 180
180 + -60t + 5t2 = 25 + 60t + -5t2 + -25 + -60t + 5t2

Reorder the terms:
180 + -60t + 5t2 = 25 + -25 + 60t + -60t + -5t2 + 5t2

Combine like terms: 25 + -25 = 0
180 + -60t + 5t2 = 0 + 60t + -60t + -5t2 + 5t2
180 + -60t + 5t2 = 60t + -60t + -5t2 + 5t2

Combine like terms: 60t + -60t = 0
180 + -60t + 5t2 = 0 + -5t2 + 5t2
180 + -60t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
180 + -60t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(36 + -12t + t2) = 0

Factor a trinomial.
5((6 + -1t)(6 + -1t)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6

Subproblem 2

Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6

Solution

t = {6, 6}

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