42=-16t^2+60t+6

Solution for 42=-16t^2+60t+6 equation:

Simplifying
42 = -16t2 + 60t + 6

Reorder the terms:
42 = 6 + 60t + -16t2

Solving
42 = 6 + 60t + -16t2

Solving for variable 't'.

Combine like terms: 42 + -6 = 36
36 + -60t + 16t2 = 6 + 60t + -16t2 + -6 + -60t + 16t2

Reorder the terms:
36 + -60t + 16t2 = 6 + -6 + 60t + -60t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
36 + -60t + 16t2 = 0 + 60t + -60t + -16t2 + 16t2
36 + -60t + 16t2 = 60t + -60t + -16t2 + 16t2

Combine like terms: 60t + -60t = 0
36 + -60t + 16t2 = 0 + -16t2 + 16t2
36 + -60t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
36 + -60t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -15t + 4t2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -4t)' equal to zero and attempt to solve:

Simplifying
3 + -4t = 0

Solving
3 + -4t = 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 + -4t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4t = 0 + -3
-4t = 0 + -3

Combine like terms: 0 + -3 = -3
-4t = -3

Divide each side by '-4'.
t = 0.75

Simplifying
t = 0.75
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 = {0.75, 3}