-3t^2+27t-42=0

Solution for -3t^2+27t-42=0 equation:

Simplifying
-3t2 + 27t + -42 = 0

Reorder the terms:
-42 + 27t + -3t2 = 0

Solving
-42 + 27t + -3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 9t + -1t2) = 0

Factor a trinomial.
3((-7 + t)(2 + -1t)) = 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 '(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 = {7, 2}