19(t-4)(t+9)=0

Solution for 19(t-4)(t+9)=0 equation:

Simplifying
19(t + -4)(t + 9) = 0

Reorder the terms:
19(-4 + t)(t + 9) = 0

Reorder the terms:
19(-4 + t)(9 + t) = 0

Multiply (-4 + t) * (9 + t)
19(-4(9 + t) + t(9 + t)) = 0
19((9 * -4 + t * -4) + t(9 + t)) = 0
19((-36 + -4t) + t(9 + t)) = 0
19(-36 + -4t + (9 * t + t * t)) = 0
19(-36 + -4t + (9t + t2)) = 0

Combine like terms: -4t + 9t = 5t
19(-36 + 5t + t2) = 0
(-36 * 19 + 5t * 19 + t2 * 19) = 0
(-684 + 95t + 19t2) = 0

Solving
-684 + 95t + 19t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '19'.
19(-36 + 5t + t2) = 0

Factor a trinomial.
19((-9 + -1t)(4 + -1t)) = 0

Ignore the factor 19.
Subproblem 1
Set the factor '(-9 + -1t)' equal to zero and attempt to solve:

Simplifying
-9 + -1t = 0

Solving
-9 + -1t = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1t = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1t = 0 + 9
-1t = 0 + 9

Combine like terms: 0 + 9 = 9
-1t = 9

Divide each side by '-1'.
t = -9

Simplifying
t = -9
Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

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

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

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

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-9, 4}