t(t-4)=32

Solution for t(t-4)=32 equation:

Simplifying
t(t + -4) = 32

Reorder the terms:
t(-4 + t) = 32
(-4 * t + t * t) = 32
(-4t + t2) = 32

Solving
-4t + t2 = 32

Solving for variable 't'.

Reorder the terms:
-32 + -4t + t2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + -4t + t2 = 0

Factor a trinomial.
(-4 + -1t)(8 + -1t) = 0

Subproblem 1
Set the factor '(-4 + -1t)' equal to zero and attempt to solve:

Simplifying
-4 + -1t = 0

Solving
-4 + -1t = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1t = 0 + 4
-1t = 0 + 4

Combine like terms: 0 + 4 = 4
-1t = 4

Divide each side by '-1'.
t = -4

Simplifying
t = -4
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 = {-4, 8}