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

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

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

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

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

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

Combine like terms: -2 + 3 = 1
1 + 2t + -6t = 3 + -5(3t + 1)

Combine like terms: 2t + -6t = -4t
1 + -4t = 3 + -5(3t + 1)

Reorder the terms:
1 + -4t = 3 + -5(1 + 3t)
1 + -4t = 3 + (1 * -5 + 3t * -5)
1 + -4t = 3 + (-5 + -15t)

Combine like terms: 3 + -5 = -2
1 + -4t = -2 + -15t

Solving
1 + -4t = -2 + -15t

Solving for variable 't'.

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

Add '15t' to each side of the equation.
1 + -4t + 15t = -2 + -15t + 15t

Combine like terms: -4t + 15t = 11t
1 + 11t = -2 + -15t + 15t

Combine like terms: -15t + 15t = 0
1 + 11t = -2 + 0
1 + 11t = -2

Add '-1' to each side of the equation.
1 + -1 + 11t = -2 + -1

Combine like terms: 1 + -1 = 0
0 + 11t = -2 + -1
11t = -2 + -1

Combine like terms: -2 + -1 = -3
11t = -3

Divide each side by '11'.
t = -0.2727272727

Simplifying
t = -0.2727272727