0=-16t^2+28t+60

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Solution for 0=-16t^2+28t+60 equation:


Simplifying
0 = -16t2 + 28t + 60

Reorder the terms:
0 = 60 + 28t + -16t2

Solving
0 = 60 + 28t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -60 = -60
-60 + -28t + 16t2 = 60 + 28t + -16t2 + -60 + -28t + 16t2

Reorder the terms:
-60 + -28t + 16t2 = 60 + -60 + 28t + -28t + -16t2 + 16t2

Combine like terms: 60 + -60 = 0
-60 + -28t + 16t2 = 0 + 28t + -28t + -16t2 + 16t2
-60 + -28t + 16t2 = 28t + -28t + -16t2 + 16t2

Combine like terms: 28t + -28t = 0
-60 + -28t + 16t2 = 0 + -16t2 + 16t2
-60 + -28t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-60 + -28t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -7t + 4t2) = 0

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

Ignore the factor 4.

Subproblem 1

Set the factor '(-5 + -4t)' equal to zero and attempt to solve: Simplifying -5 + -4t = 0 Solving -5 + -4t = 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 + -4t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4t = 0 + 5 -4t = 0 + 5 Combine like terms: 0 + 5 = 5 -4t = 5 Divide each side by '-4'. t = -1.25 Simplifying t = -1.25

Subproblem 2

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

Solution

t = {-1.25, 3}

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