2(t+2)-6(1-3t)=19(t+1)+2

Solution for 2(t+2)-6(1-3t)=19(t+1)+2 equation:

Simplifying
2(t + 2) + -6(1 + -3t) = 19(t + 1) + 2

Reorder the terms:
2(2 + t) + -6(1 + -3t) = 19(t + 1) + 2
(2 * 2 + t * 2) + -6(1 + -3t) = 19(t + 1) + 2
(4 + 2t) + -6(1 + -3t) = 19(t + 1) + 2
4 + 2t + (1 * -6 + -3t * -6) = 19(t + 1) + 2
4 + 2t + (-6 + 18t) = 19(t + 1) + 2

Reorder the terms:
4 + -6 + 2t + 18t = 19(t + 1) + 2

Combine like terms: 4 + -6 = -2
-2 + 2t + 18t = 19(t + 1) + 2

Combine like terms: 2t + 18t = 20t
-2 + 20t = 19(t + 1) + 2

Reorder the terms:
-2 + 20t = 19(1 + t) + 2
-2 + 20t = (1 * 19 + t * 19) + 2
-2 + 20t = (19 + 19t) + 2

Reorder the terms:
-2 + 20t = 19 + 2 + 19t

Combine like terms: 19 + 2 = 21
-2 + 20t = 21 + 19t

Solving
-2 + 20t = 21 + 19t

Solving for variable 't'.

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

Add '-19t' to each side of the equation.
-2 + 20t + -19t = 21 + 19t + -19t

Combine like terms: 20t + -19t = 1t
-2 + 1t = 21 + 19t + -19t

Combine like terms: 19t + -19t = 0
-2 + 1t = 21 + 0
-2 + 1t = 21

Add '2' to each side of the equation.
-2 + 2 + 1t = 21 + 2

Combine like terms: -2 + 2 = 0
0 + 1t = 21 + 2
1t = 21 + 2

Combine like terms: 21 + 2 = 23
1t = 23

Divide each side by '1'.
t = 23

Simplifying
t = 23