60=5t+5t^2

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Solution for 60=5t+5t^2 equation:


Simplifying
60 = 5t + 5t2

Solving
60 = 5t + 5t2

Solving for variable 't'.

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

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

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

Factor out the Greatest Common Factor (GCF), '5'.
5(12 + -1t + -1t2) = 0

Factor a trinomial.
5((3 + -1t)(4 + t)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3

Subproblem 2

Set the factor '(4 + t)' equal to zero and attempt to solve: Simplifying 4 + t = 0 Solving 4 + t = 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 + t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + t = 0 + -4 t = 0 + -4 Combine like terms: 0 + -4 = -4 t = -4 Simplifying t = -4

Solution

t = {3, -4}

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