(7t-2)-(3t+1)=3(1-3t)

Solution for (7t-2)-(3t+1)=3(1-3t) equation:

Simplifying
(7t + -2) + -1(3t + 1) = 3(1 + -3t)

Reorder the terms:
(-2 + 7t) + -1(3t + 1) = 3(1 + -3t)

Remove parenthesis around (-2 + 7t)
-2 + 7t + -1(3t + 1) = 3(1 + -3t)

Reorder the terms:
-2 + 7t + -1(1 + 3t) = 3(1 + -3t)
-2 + 7t + (1 * -1 + 3t * -1) = 3(1 + -3t)
-2 + 7t + (-1 + -3t) = 3(1 + -3t)

Reorder the terms:
-2 + -1 + 7t + -3t = 3(1 + -3t)

Combine like terms: -2 + -1 = -3
-3 + 7t + -3t = 3(1 + -3t)

Combine like terms: 7t + -3t = 4t
-3 + 4t = 3(1 + -3t)
-3 + 4t = (1 * 3 + -3t * 3)
-3 + 4t = (3 + -9t)

Solving
-3 + 4t = 3 + -9t

Solving for variable 't'.

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

Add '9t' to each side of the equation.
-3 + 4t + 9t = 3 + -9t + 9t

Combine like terms: 4t + 9t = 13t
-3 + 13t = 3 + -9t + 9t

Combine like terms: -9t + 9t = 0
-3 + 13t = 3 + 0
-3 + 13t = 3

Add '3' to each side of the equation.
-3 + 3 + 13t = 3 + 3

Combine like terms: -3 + 3 = 0
0 + 13t = 3 + 3
13t = 3 + 3

Combine like terms: 3 + 3 = 6
13t = 6

Divide each side by '13'.
t = 0.4615384615

Simplifying
t = 0.4615384615