8(5-t)+2=-2(t-4)-3

Solution for 8(5-t)+2=-2(t-4)-3 equation:

Simplifying
8(5 + -1t) + 2 = -2(t + -4) + -3
(5 * 8 + -1t * 8) + 2 = -2(t + -4) + -3
(40 + -8t) + 2 = -2(t + -4) + -3

Reorder the terms:
40 + 2 + -8t = -2(t + -4) + -3

Combine like terms: 40 + 2 = 42
42 + -8t = -2(t + -4) + -3

Reorder the terms:
42 + -8t = -2(-4 + t) + -3
42 + -8t = (-4 * -2 + t * -2) + -3
42 + -8t = (8 + -2t) + -3

Reorder the terms:
42 + -8t = 8 + -3 + -2t

Combine like terms: 8 + -3 = 5
42 + -8t = 5 + -2t

Solving
42 + -8t = 5 + -2t

Solving for variable 't'.

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

Add '2t' to each side of the equation.
42 + -8t + 2t = 5 + -2t + 2t

Combine like terms: -8t + 2t = -6t
42 + -6t = 5 + -2t + 2t

Combine like terms: -2t + 2t = 0
42 + -6t = 5 + 0
42 + -6t = 5

Add '-42' to each side of the equation.
42 + -42 + -6t = 5 + -42

Combine like terms: 42 + -42 = 0
0 + -6t = 5 + -42
-6t = 5 + -42

Combine like terms: 5 + -42 = -37
-6t = -37

Divide each side by '-6'.
t = 6.166666667

Simplifying
t = 6.166666667