0=-16t^2+60t+100

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Solution for 0=-16t^2+60t+100 equation: 


Simplifying
0 = -16t2 + 60t + 100

Reorder the terms:
0 = 100 + 60t + -16t2

Solving
0 = 100 + 60t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -100 = -100
-100 + -60t + 16t2 = 100 + 60t + -16t2 + -100 + -60t + 16t2

Reorder the terms:
-100 + -60t + 16t2 = 100 + -100 + 60t + -60t + -16t2 + 16t2

Combine like terms: 100 + -100 = 0
-100 + -60t + 16t2 = 0 + 60t + -60t + -16t2 + 16t2
-100 + -60t + 16t2 = 60t + -60t + -16t2 + 16t2

Combine like terms: 60t + -60t = 0
-100 + -60t + 16t2 = 0 + -16t2 + 16t2
-100 + -60t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-100 + -60t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-25 + -15t + 4t2) = 0

Factor a trinomial.
4((-5 + -4t)(5 + -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 '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 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 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-1.25, 5}

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