(t-6)(t-1)=0

Solution for (t-6)(t-1)=0 equation:

Simplifying
(t + -6)(t + -1) = 0

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

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

Multiply (-6 + t) * (-1 + t)
(-6(-1 + t) + t(-1 + t)) = 0
((-1 * -6 + t * -6) + t(-1 + t)) = 0
((6 + -6t) + t(-1 + t)) = 0
(6 + -6t + (-1 * t + t * t)) = 0
(6 + -6t + (-1t + t2)) = 0

Combine like terms: -6t + -1t = -7t
(6 + -7t + t2) = 0

Solving
6 + -7t + t2 = 0

Solving for variable 't'.

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

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

Simplifying
1 + -1t = 0

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

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

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

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

Simplifying
t = 1
Subproblem 2
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
Solution
t = {1, 6}