45t-21-6t^2=0

Solution for 45t-21-6t^2=0 equation:

Simplifying
45t + -21 + -6t2 = 0

Reorder the terms:
-21 + 45t + -6t2 = 0

Solving
-21 + 45t + -6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 15t + -2t2) = 0

Factor a trinomial.
3((-7 + t)(1 + -2t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + t)' equal to zero and attempt to solve:

Simplifying
-7 + t = 0

Solving
-7 + t = 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 + t = 0 + 7

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

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

Simplifying
t = 7
Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

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

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

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Solution
t = {7, 0.5}