2(2t+3)=8(t-1)-5(t-2)

Solution for 2(2t+3)=8(t-1)-5(t-2) equation:

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

Reorder the terms:
2(3 + 2t) = 8(t + -1) + -5(t + -2)
(3 * 2 + 2t * 2) = 8(t + -1) + -5(t + -2)
(6 + 4t) = 8(t + -1) + -5(t + -2)

Reorder the terms:
6 + 4t = 8(-1 + t) + -5(t + -2)
6 + 4t = (-1 * 8 + t * 8) + -5(t + -2)
6 + 4t = (-8 + 8t) + -5(t + -2)

Reorder the terms:
6 + 4t = -8 + 8t + -5(-2 + t)
6 + 4t = -8 + 8t + (-2 * -5 + t * -5)
6 + 4t = -8 + 8t + (10 + -5t)

Reorder the terms:
6 + 4t = -8 + 10 + 8t + -5t

Combine like terms: -8 + 10 = 2
6 + 4t = 2 + 8t + -5t

Combine like terms: 8t + -5t = 3t
6 + 4t = 2 + 3t

Solving
6 + 4t = 2 + 3t

Solving for variable 't'.

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

Add '-3t' to each side of the equation.
6 + 4t + -3t = 2 + 3t + -3t

Combine like terms: 4t + -3t = 1t
6 + 1t = 2 + 3t + -3t

Combine like terms: 3t + -3t = 0
6 + 1t = 2 + 0
6 + 1t = 2

Add '-6' to each side of the equation.
6 + -6 + 1t = 2 + -6

Combine like terms: 6 + -6 = 0
0 + 1t = 2 + -6
1t = 2 + -6

Combine like terms: 2 + -6 = -4
1t = -4

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

Simplifying
t = -4