t^2(7t+6)=0

Solution for t^2(7t+6)=0 equation:

Simplifying
t2(7t + 6) = 0

Reorder the terms:
t2(6 + 7t) = 0
(6 * t2 + 7t * t2) = 0
(6t2 + 7t3) = 0

Solving
6t2 + 7t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't2'.
t2(6 + 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 '(6 + 7t)' equal to zero and attempt to solve:

Simplifying
6 + 7t = 0

Solving
6 + 7t = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7t = 0 + -6
7t = 0 + -6

Combine like terms: 0 + -6 = -6
7t = -6

Divide each side by '7'.
t = -0.8571428571

Simplifying
t = -0.8571428571
Solution
t = {0, -0.8571428571}