t(t-7)=8

Solution for t(t-7)=8 equation:

Simplifying
t(t + -7) = 8

Reorder the terms:
t(-7 + t) = 8
(-7 * t + t * t) = 8
(-7t + t2) = 8

Solving
-7t + t2 = 8

Solving for variable 't'.

Reorder the terms:
-8 + -7t + t2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -7t + t2 = 0

Factor a trinomial.
(-1 + -1t)(8 + -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 '(8 + -1t)' equal to zero and attempt to solve:

Simplifying
8 + -1t = 0

Solving
8 + -1t = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1t = 0 + -8
-1t = 0 + -8

Combine like terms: 0 + -8 = -8
-1t = -8

Divide each side by '-1'.
t = 8

Simplifying
t = 8
Solution
t = {-1, 8}