2(t-1)-3(4t-1)=3-5(6t+1)

Solution for 2(t-1)-3(4t-1)=3-5(6t+1) equation:

Simplifying
2(t + -1) + -3(4t + -1) = 3 + -5(6t + 1)

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

Reorder the terms:
-2 + 2t + -3(-1 + 4t) = 3 + -5(6t + 1)
-2 + 2t + (-1 * -3 + 4t * -3) = 3 + -5(6t + 1)
-2 + 2t + (3 + -12t) = 3 + -5(6t + 1)

Reorder the terms:
-2 + 3 + 2t + -12t = 3 + -5(6t + 1)

Combine like terms: -2 + 3 = 1
1 + 2t + -12t = 3 + -5(6t + 1)

Combine like terms: 2t + -12t = -10t
1 + -10t = 3 + -5(6t + 1)

Reorder the terms:
1 + -10t = 3 + -5(1 + 6t)
1 + -10t = 3 + (1 * -5 + 6t * -5)
1 + -10t = 3 + (-5 + -30t)

Combine like terms: 3 + -5 = -2
1 + -10t = -2 + -30t

Solving
1 + -10t = -2 + -30t

Solving for variable 't'.

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

Add '30t' to each side of the equation.
1 + -10t + 30t = -2 + -30t + 30t

Combine like terms: -10t + 30t = 20t
1 + 20t = -2 + -30t + 30t

Combine like terms: -30t + 30t = 0
1 + 20t = -2 + 0
1 + 20t = -2

Add '-1' to each side of the equation.
1 + -1 + 20t = -2 + -1

Combine like terms: 1 + -1 = 0
0 + 20t = -2 + -1
20t = -2 + -1

Combine like terms: -2 + -1 = -3
20t = -3

Divide each side by '20'.
t = -0.15

Simplifying
t = -0.15