144t-16t^2=288

Solution for 144t-16t^2=288 equation:

Simplifying
144t + -16t2 = 288

Solving
144t + -16t2 = 288

Solving for variable 't'.

Reorder the terms:
-288 + 144t + -16t2 = 288 + -288

Combine like terms: 288 + -288 = 0
-288 + 144t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-18 + 9t + -1t2) = 0

Factor a trinomial.
16((-6 + t)(3 + -1t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-6 + t)' equal to zero and attempt to solve:

Simplifying
-6 + t = 0

Solving
-6 + t = 0

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

Add '6' to each side of the equation.
-6 + 6 + t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + t = 0 + 6
t = 0 + 6

Combine like terms: 0 + 6 = 6
t = 6

Simplifying
t = 6
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 = {6, 3}