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

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

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

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

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

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

Combine like terms: 3 + 1 = 4
-2 + 7t + -1(4 + -1t) = -3(1 + -3t)
-2 + 7t + (4 * -1 + -1t * -1) = -3(1 + -3t)
-2 + 7t + (-4 + 1t) = -3(1 + -3t)

Reorder the terms:
-2 + -4 + 7t + 1t = -3(1 + -3t)

Combine like terms: -2 + -4 = -6
-6 + 7t + 1t = -3(1 + -3t)

Combine like terms: 7t + 1t = 8t
-6 + 8t = -3(1 + -3t)
-6 + 8t = (1 * -3 + -3t * -3)
-6 + 8t = (-3 + 9t)

Solving
-6 + 8t = -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.
-6 + 8t + -9t = -3 + 9t + -9t

Combine like terms: 8t + -9t = -1t
-6 + -1t = -3 + 9t + -9t

Combine like terms: 9t + -9t = 0
-6 + -1t = -3 + 0
-6 + -1t = -3

Add '6' to each side of the equation.
-6 + 6 + -1t = -3 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = -3 + 6
-1t = -3 + 6

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

Divide each side by '-1'.
t = -3

Simplifying
t = -3