9=-16t^2+36t+1

Solution for 9=-16t^2+36t+1 equation:

Simplifying
9 = -16t2 + 36t + 1

Reorder the terms:
9 = 1 + 36t + -16t2

Solving
9 = 1 + 36t + -16t2

Solving for variable 't'.

Combine like terms: 9 + -1 = 8
8 + -36t + 16t2 = 1 + 36t + -16t2 + -1 + -36t + 16t2

Reorder the terms:
8 + -36t + 16t2 = 1 + -1 + 36t + -36t + -16t2 + 16t2

Combine like terms: 1 + -1 = 0
8 + -36t + 16t2 = 0 + 36t + -36t + -16t2 + 16t2
8 + -36t + 16t2 = 36t + -36t + -16t2 + 16t2

Combine like terms: 36t + -36t = 0
8 + -36t + 16t2 = 0 + -16t2 + 16t2
8 + -36t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
8 + -36t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + -9t + 4t2) = 0

Factor a trinomial.
4((1 + -4t)(2 + -1t)) = 0

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

Simplifying
1 + -4t = 0

Solving
1 + -4t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4t = 0 + -1
-4t = 0 + -1

Combine like terms: 0 + -1 = -1
-4t = -1

Divide each side by '-4'.
t = 0.25

Simplifying
t = 0.25
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {0.25, 2}