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

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

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

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

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

Reorder the terms:
-3 + -6 + 3t + -4t = 5(t + 3)

Combine like terms: -3 + -6 = -9
-9 + 3t + -4t = 5(t + 3)

Combine like terms: 3t + -4t = -1t
-9 + -1t = 5(t + 3)

Reorder the terms:
-9 + -1t = 5(3 + t)
-9 + -1t = (3 * 5 + t * 5)
-9 + -1t = (15 + 5t)

Solving
-9 + -1t = 15 + 5t

Solving for variable 't'.

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

Add '-5t' to each side of the equation.
-9 + -1t + -5t = 15 + 5t + -5t

Combine like terms: -1t + -5t = -6t
-9 + -6t = 15 + 5t + -5t

Combine like terms: 5t + -5t = 0
-9 + -6t = 15 + 0
-9 + -6t = 15

Add '9' to each side of the equation.
-9 + 9 + -6t = 15 + 9

Combine like terms: -9 + 9 = 0
0 + -6t = 15 + 9
-6t = 15 + 9

Combine like terms: 15 + 9 = 24
-6t = 24

Divide each side by '-6'.
t = -4

Simplifying
t = -4