(t+4)(4)+(t+4)(4)=(t-4)(t+4)(5)

Solution for (t+4)(4)+(t+4)(4)=(t-4)(t+4)(5) equation:

Simplifying
(t + 4)(4) + (t + 4)(4) = (t + -4)(t + 4)(5)

Reorder the terms:
(4 + t)(4) + (t + 4)(4) = (t + -4)(t + 4)(5)

Reorder the terms for easier multiplication:
4(4 + t) + (t + 4)(4) = (t + -4)(t + 4)(5)
(4 * 4 + t * 4) + (t + 4)(4) = (t + -4)(t + 4)(5)
(16 + 4t) + (t + 4)(4) = (t + -4)(t + 4)(5)

Reorder the terms:
16 + 4t + (4 + t)(4) = (t + -4)(t + 4)(5)

Reorder the terms for easier multiplication:
16 + 4t + 4(4 + t) = (t + -4)(t + 4)(5)
16 + 4t + (4 * 4 + t * 4) = (t + -4)(t + 4)(5)
16 + 4t + (16 + 4t) = (t + -4)(t + 4)(5)

Reorder the terms:
16 + 16 + 4t + 4t = (t + -4)(t + 4)(5)

Combine like terms: 16 + 16 = 32
32 + 4t + 4t = (t + -4)(t + 4)(5)

Combine like terms: 4t + 4t = 8t
32 + 8t = (t + -4)(t + 4)(5)

Reorder the terms:
32 + 8t = (-4 + t)(t + 4)(5)

Reorder the terms:
32 + 8t = (-4 + t)(4 + t)(5)

Reorder the terms for easier multiplication:
32 + 8t = 5(-4 + t)(4 + t)

Multiply (-4 + t) * (4 + t)
32 + 8t = 5(-4(4 + t) + t(4 + t))
32 + 8t = 5((4 * -4 + t * -4) + t(4 + t))
32 + 8t = 5((-16 + -4t) + t(4 + t))
32 + 8t = 5(-16 + -4t + (4 * t + t * t))
32 + 8t = 5(-16 + -4t + (4t + t2))

Combine like terms: -4t + 4t = 0
32 + 8t = 5(-16 + 0 + t2)
32 + 8t = 5(-16 + t2)
32 + 8t = (-16 * 5 + t2 * 5)
32 + 8t = (-80 + 5t2)

Solving
32 + 8t = -80 + 5t2

Solving for variable 't'.

Reorder the terms:
32 + 80 + 8t + -5t2 = -80 + 5t2 + 80 + -5t2

Combine like terms: 32 + 80 = 112
112 + 8t + -5t2 = -80 + 5t2 + 80 + -5t2

Reorder the terms:
112 + 8t + -5t2 = -80 + 80 + 5t2 + -5t2

Combine like terms: -80 + 80 = 0
112 + 8t + -5t2 = 0 + 5t2 + -5t2
112 + 8t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
112 + 8t + -5t2 = 0

Factor a trinomial.
(28 + -5t)(4 + t) = 0

Subproblem 1
Set the factor '(28 + -5t)' equal to zero and attempt to solve:

Simplifying
28 + -5t = 0

Solving
28 + -5t = 0

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

Add '-28' to each side of the equation.
28 + -28 + -5t = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -5t = 0 + -28
-5t = 0 + -28

Combine like terms: 0 + -28 = -28
-5t = -28

Divide each side by '-5'.
t = 5.6

Simplifying
t = 5.6
Subproblem 2
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
Solution
t = {5.6, -4}