-4t^2+24t+6=42

Solution for -4t^2+24t+6=42 equation:

Simplifying
-4t2 + 24t + 6 = 42

Reorder the terms:
6 + 24t + -4t2 = 42

Solving
6 + 24t + -4t2 = 42

Solving for variable 't'.

Reorder the terms:
6 + -42 + 24t + -4t2 = 42 + -42

Combine like terms: 6 + -42 = -36
-36 + 24t + -4t2 = 42 + -42

Combine like terms: 42 + -42 = 0
-36 + 24t + -4t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + 6t + -1t2) = 0

Factor a trinomial.
4((-3 + t)(3 + -1t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + t)' equal to zero and attempt to solve:

Simplifying
-3 + t = 0

Solving
-3 + t = 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 + t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + t = 0 + 3
t = 0 + 3

Combine like terms: 0 + 3 = 3
t = 3

Simplifying
t = 3
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 = {3, 3}