120=-5t^2+60t+65

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Solution for 120=-5t^2+60t+65 equation:


Simplifying
120 = -5t2 + 60t + 65

Reorder the terms:
120 = 65 + 60t + -5t2

Solving
120 = 65 + 60t + -5t2

Solving for variable 't'.

Combine like terms: 120 + -65 = 55
55 + -60t + 5t2 = 65 + 60t + -5t2 + -65 + -60t + 5t2

Reorder the terms:
55 + -60t + 5t2 = 65 + -65 + 60t + -60t + -5t2 + 5t2

Combine like terms: 65 + -65 = 0
55 + -60t + 5t2 = 0 + 60t + -60t + -5t2 + 5t2
55 + -60t + 5t2 = 60t + -60t + -5t2 + 5t2

Combine like terms: 60t + -60t = 0
55 + -60t + 5t2 = 0 + -5t2 + 5t2
55 + -60t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
55 + -60t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(11 + -12t + t2) = 0

Factor a trinomial.
5((1 + -1t)(11 + -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 '(11 + -1t)' equal to zero and attempt to solve: Simplifying 11 + -1t = 0 Solving 11 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1t = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1t = 0 + -11 -1t = 0 + -11 Combine like terms: 0 + -11 = -11 -1t = -11 Divide each side by '-1'. t = 11 Simplifying t = 11

Solution

t = {1, 11}

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