42=-16t^2+48t+6

Solution for 42=-16t^2+48t+6 equation:

Simplifying
42 = -16t2 + 48t + 6

Reorder the terms:
42 = 6 + 48t + -16t2

Solving
42 = 6 + 48t + -16t2

Solving for variable 't'.

Combine like terms: 42 + -6 = 36
36 + -48t + 16t2 = 6 + 48t + -16t2 + -6 + -48t + 16t2

Reorder the terms:
36 + -48t + 16t2 = 6 + -6 + 48t + -48t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
36 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2
36 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2

Combine like terms: 48t + -48t = 0
36 + -48t + 16t2 = 0 + -16t2 + 16t2
36 + -48t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
36 + -48t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -12t + 4t2) = 0

Factor a trinomial.
4((3 + -2t)(3 + -2t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 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 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 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 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Solution
t = {1.5, 1.5}