(t-1)(t+7)=0

Solution for (t-1)(t+7)=0 equation:

Simplifying
(t + -1)(t + 7) = 0

Reorder the terms:
(-1 + t)(t + 7) = 0

Reorder the terms:
(-1 + t)(7 + t) = 0

Multiply (-1 + t) * (7 + t)
(-1(7 + t) + t(7 + t)) = 0
((7 * -1 + t * -1) + t(7 + t)) = 0
((-7 + -1t) + t(7 + t)) = 0
(-7 + -1t + (7 * t + t * t)) = 0
(-7 + -1t + (7t + t2)) = 0

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

Solving
-7 + 6t + t2 = 0

Solving for variable 't'.

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

Subproblem 1
Set the factor '(-7 + -1t)' equal to zero and attempt to solve:

Simplifying
-7 + -1t = 0

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

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

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

Divide each side by '-1'.
t = -7

Simplifying
t = -7
Subproblem 2
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
Solution
t = {-7, 1}