2(3t-1)+13=4(t-1)-(3t+2)

Solution for 2(3t-1)+13=4(t-1)-(3t+2) equation:

Simplifying
2(3t + -1) + 13 = 4(t + -1) + -1(3t + 2)

Reorder the terms:
2(-1 + 3t) + 13 = 4(t + -1) + -1(3t + 2)
(-1 * 2 + 3t * 2) + 13 = 4(t + -1) + -1(3t + 2)
(-2 + 6t) + 13 = 4(t + -1) + -1(3t + 2)

Reorder the terms:
-2 + 13 + 6t = 4(t + -1) + -1(3t + 2)

Combine like terms: -2 + 13 = 11
11 + 6t = 4(t + -1) + -1(3t + 2)

Reorder the terms:
11 + 6t = 4(-1 + t) + -1(3t + 2)
11 + 6t = (-1 * 4 + t * 4) + -1(3t + 2)
11 + 6t = (-4 + 4t) + -1(3t + 2)

Reorder the terms:
11 + 6t = -4 + 4t + -1(2 + 3t)
11 + 6t = -4 + 4t + (2 * -1 + 3t * -1)
11 + 6t = -4 + 4t + (-2 + -3t)

Reorder the terms:
11 + 6t = -4 + -2 + 4t + -3t

Combine like terms: -4 + -2 = -6
11 + 6t = -6 + 4t + -3t

Combine like terms: 4t + -3t = 1t
11 + 6t = -6 + 1t

Solving
11 + 6t = -6 + 1t

Solving for variable 't'.

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

Add '-1t' to each side of the equation.
11 + 6t + -1t = -6 + 1t + -1t

Combine like terms: 6t + -1t = 5t
11 + 5t = -6 + 1t + -1t

Combine like terms: 1t + -1t = 0
11 + 5t = -6 + 0
11 + 5t = -6

Add '-11' to each side of the equation.
11 + -11 + 5t = -6 + -11

Combine like terms: 11 + -11 = 0
0 + 5t = -6 + -11
5t = -6 + -11

Combine like terms: -6 + -11 = -17
5t = -17

Divide each side by '5'.
t = -3.4

Simplifying
t = -3.4