(t-2)4+(3t+14)8=(t+2)16

Solution for (t-2)4+(3t+14)8=(t+2)16 equation:

Simplifying
(t + -2) * 4 + (3t + 14) * 8 = (t + 2) * 16

Reorder the terms:
(-2 + t) * 4 + (3t + 14) * 8 = (t + 2) * 16

Reorder the terms for easier multiplication:
4(-2 + t) + (3t + 14) * 8 = (t + 2) * 16
(-2 * 4 + t * 4) + (3t + 14) * 8 = (t + 2) * 16
(-8 + 4t) + (3t + 14) * 8 = (t + 2) * 16

Reorder the terms:
-8 + 4t + (14 + 3t) * 8 = (t + 2) * 16

Reorder the terms for easier multiplication:
-8 + 4t + 8(14 + 3t) = (t + 2) * 16
-8 + 4t + (14 * 8 + 3t * 8) = (t + 2) * 16
-8 + 4t + (112 + 24t) = (t + 2) * 16

Reorder the terms:
-8 + 112 + 4t + 24t = (t + 2) * 16

Combine like terms: -8 + 112 = 104
104 + 4t + 24t = (t + 2) * 16

Combine like terms: 4t + 24t = 28t
104 + 28t = (t + 2) * 16

Reorder the terms:
104 + 28t = (2 + t) * 16

Reorder the terms for easier multiplication:
104 + 28t = 16(2 + t)
104 + 28t = (2 * 16 + t * 16)
104 + 28t = (32 + 16t)

Solving
104 + 28t = 32 + 16t

Solving for variable 't'.

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

Add '-16t' to each side of the equation.
104 + 28t + -16t = 32 + 16t + -16t

Combine like terms: 28t + -16t = 12t
104 + 12t = 32 + 16t + -16t

Combine like terms: 16t + -16t = 0
104 + 12t = 32 + 0
104 + 12t = 32

Add '-104' to each side of the equation.
104 + -104 + 12t = 32 + -104

Combine like terms: 104 + -104 = 0
0 + 12t = 32 + -104
12t = 32 + -104

Combine like terms: 32 + -104 = -72
12t = -72

Divide each side by '12'.
t = -6

Simplifying
t = -6