t^2(-14t^2+19t+3)=0

Solution for t^2(-14t^2+19t+3)=0 equation:

Simplifying
t2(-14t2 + 19t + 3) = 0

Reorder the terms:
t2(3 + 19t + -14t2) = 0
(3 * t2 + 19t * t2 + -14t2 * t2) = 0
(3t2 + 19t3 + -14t4) = 0

Solving
3t2 + 19t3 + -14t4 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't2'.
t2(3 + 19t + -14t2) = 0

Factor a trinomial.
t2((3 + -2t)(1 + 7t)) = 0

Subproblem 1
Set the factor 't2' equal to zero and attempt to solve:

Simplifying
t2 = 0

Solving
t2 = 0

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

Simplifying
t2 = 0

Take the square root of each side:
t = {0}
Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 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 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Subproblem 3
Set the factor '(1 + 7t)' equal to zero and attempt to solve:

Simplifying
1 + 7t = 0

Solving
1 + 7t = 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 + 7t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7t = 0 + -1
7t = 0 + -1

Combine like terms: 0 + -1 = -1
7t = -1

Divide each side by '7'.
t = -0.1428571429

Simplifying
t = -0.1428571429
Solution
t = {0, 1.5, -0.1428571429}