2(t+3)=5(t-1)-7(t-3)

Solution for 2(t+3)=5(t-1)-7(t-3) equation:

Simplifying
2(t + 3) = 5(t + -1) + -7(t + -3)

Reorder the terms:
2(3 + t) = 5(t + -1) + -7(t + -3)
(3 * 2 + t * 2) = 5(t + -1) + -7(t + -3)
(6 + 2t) = 5(t + -1) + -7(t + -3)

Reorder the terms:
6 + 2t = 5(-1 + t) + -7(t + -3)
6 + 2t = (-1 * 5 + t * 5) + -7(t + -3)
6 + 2t = (-5 + 5t) + -7(t + -3)

Reorder the terms:
6 + 2t = -5 + 5t + -7(-3 + t)
6 + 2t = -5 + 5t + (-3 * -7 + t * -7)
6 + 2t = -5 + 5t + (21 + -7t)

Reorder the terms:
6 + 2t = -5 + 21 + 5t + -7t

Combine like terms: -5 + 21 = 16
6 + 2t = 16 + 5t + -7t

Combine like terms: 5t + -7t = -2t
6 + 2t = 16 + -2t

Solving
6 + 2t = 16 + -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.
6 + 2t + 2t = 16 + -2t + 2t

Combine like terms: 2t + 2t = 4t
6 + 4t = 16 + -2t + 2t

Combine like terms: -2t + 2t = 0
6 + 4t = 16 + 0
6 + 4t = 16

Add '-6' to each side of the equation.
6 + -6 + 4t = 16 + -6

Combine like terms: 6 + -6 = 0
0 + 4t = 16 + -6
4t = 16 + -6

Combine like terms: 16 + -6 = 10
4t = 10

Divide each side by '4'.
t = 2.5

Simplifying
t = 2.5