6+40t-16t^2=27

Solution for 6+40t-16t^2=27 equation:

Simplifying
6 + 40t + -16t2 = 27

Solving
6 + 40t + -16t2 = 27

Solving for variable 't'.

Reorder the terms:
6 + -27 + 40t + -16t2 = 27 + -27

Combine like terms: 6 + -27 = -21
-21 + 40t + -16t2 = 27 + -27

Combine like terms: 27 + -27 = 0
-21 + 40t + -16t2 = 0

Factor a trinomial.
(-7 + 4t)(3 + -4t) = 0

Subproblem 1
Set the factor '(-7 + 4t)' equal to zero and attempt to solve:

Simplifying
-7 + 4t = 0

Solving
-7 + 4t = 0

Move all terms containing t to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + 4t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4t = 0 + 7
4t = 0 + 7

Combine like terms: 0 + 7 = 7
4t = 7

Divide each side by '4'.
t = 1.75

Simplifying
t = 1.75
Subproblem 2
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
Solution
t = {1.75, 0.75}