16(t-1)=t(t+8)

Solution for 16(t-1)=t(t+8) equation:

Simplifying
16(t + -1) = t(t + 8)

Reorder the terms:
16(-1 + t) = t(t + 8)
(-1 * 16 + t * 16) = t(t + 8)
(-16 + 16t) = t(t + 8)

Reorder the terms:
-16 + 16t = t(8 + t)
-16 + 16t = (8 * t + t * t)
-16 + 16t = (8t + t2)

Solving
-16 + 16t = 8t + t2

Solving for variable 't'.

Combine like terms: 16t + -8t = 8t
-16 + 8t + -1t2 = 8t + t2 + -8t + -1t2

Reorder the terms:
-16 + 8t + -1t2 = 8t + -8t + t2 + -1t2

Combine like terms: 8t + -8t = 0
-16 + 8t + -1t2 = 0 + t2 + -1t2
-16 + 8t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-16 + 8t + -1t2 = 0

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

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

Simplifying
-4 + t = 0

Solving
-4 + t = 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 + t = 0 + 4

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

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

Simplifying
t = 4
Subproblem 2
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
Solution
t = {4, 4}