(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 = 10t
-3 + 10t = 3(1 + 3t)
-3 + 10t = (1 * 3 + 3t * 3)
-3 + 10t = (3 + 9t)

Solving
-3 + 10t = 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 + 10t + -9t = 3 + 9t + -9t

Combine like terms: 10t + -9t = 1t
-3 + 1t = 3 + 9t + -9t

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

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

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

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

Divide each side by '1'.
t = 6

Simplifying
t = 6