(6t-7)(t+6)=0

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

Simplifying
(6t + -7)(t + 6) = 0

Reorder the terms:
(-7 + 6t)(t + 6) = 0

Reorder the terms:
(-7 + 6t)(6 + t) = 0

Multiply (-7 + 6t) * (6 + t)
(-7(6 + t) + 6t * (6 + t)) = 0
((6 * -7 + t * -7) + 6t * (6 + t)) = 0
((-42 + -7t) + 6t * (6 + t)) = 0
(-42 + -7t + (6 * 6t + t * 6t)) = 0
(-42 + -7t + (36t + 6t2)) = 0

Combine like terms: -7t + 36t = 29t
(-42 + 29t + 6t2) = 0

Solving
-42 + 29t + 6t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-6 + -1t)(7 + -6t) = 0

Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

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

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

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

Divide each side by '-1'.
t = -6

Simplifying
t = -6
Subproblem 2
Set the factor '(7 + -6t)' equal to zero and attempt to solve:

Simplifying
7 + -6t = 0

Solving
7 + -6t = 0

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

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

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

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

Divide each side by '-6'.
t = 1.166666667

Simplifying
t = 1.166666667
Solution
t = {-6, 1.166666667}