=t(6t+1)

Solution for =t(6t+1) equation:

Simplifying
0 = t(6t + 1)

Reorder the terms:
0 = t(1 + 6t)
0 = (1 * t + 6t * t)
0 = (1t + 6t2)

Solving
0 = 1t + 6t2

Solving for variable 't'.
Remove the zero:
-1t + -6t2 = 1t + 6t2 + -1t + -6t2

Reorder the terms:
-1t + -6t2 = 1t + -1t + 6t2 + -6t2

Combine like terms: 1t + -1t = 0
-1t + -6t2 = 0 + 6t2 + -6t2
-1t + -6t2 = 6t2 + -6t2

Combine like terms: 6t2 + -6t2 = 0
-1t + -6t2 = 0

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

Ignore the factor -1.
Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(1 + 6t)' equal to zero and attempt to solve:

Simplifying
1 + 6t = 0

Solving
1 + 6t = 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 + 6t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6t = 0 + -1
6t = 0 + -1

Combine like terms: 0 + -1 = -1
6t = -1

Divide each side by '6'.
t = -0.1666666667

Simplifying
t = -0.1666666667
Solution
t = {0, -0.1666666667}