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

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

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

Reorder the terms:
6(-2 + t) + -5(1 + -3t) = 2(t + 1)
(-2 * 6 + t * 6) + -5(1 + -3t) = 2(t + 1)
(-12 + 6t) + -5(1 + -3t) = 2(t + 1)
-12 + 6t + (1 * -5 + -3t * -5) = 2(t + 1)
-12 + 6t + (-5 + 15t) = 2(t + 1)

Reorder the terms:
-12 + -5 + 6t + 15t = 2(t + 1)

Combine like terms: -12 + -5 = -17
-17 + 6t + 15t = 2(t + 1)

Combine like terms: 6t + 15t = 21t
-17 + 21t = 2(t + 1)

Reorder the terms:
-17 + 21t = 2(1 + t)
-17 + 21t = (1 * 2 + t * 2)
-17 + 21t = (2 + 2t)

Solving
-17 + 21t = 2 + 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.
-17 + 21t + -2t = 2 + 2t + -2t

Combine like terms: 21t + -2t = 19t
-17 + 19t = 2 + 2t + -2t

Combine like terms: 2t + -2t = 0
-17 + 19t = 2 + 0
-17 + 19t = 2

Add '17' to each side of the equation.
-17 + 17 + 19t = 2 + 17

Combine like terms: -17 + 17 = 0
0 + 19t = 2 + 17
19t = 2 + 17

Combine like terms: 2 + 17 = 19
19t = 19

Divide each side by '19'.
t = 1

Simplifying
t = 1