(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)

Add '3' to each side of the equation.
-3 + 3 + 10t = -3 + 3 + -9t

Combine like terms: -3 + 3 = 0
0 + 10t = -3 + 3 + -9t
10t = -3 + 3 + -9t

Combine like terms: -3 + 3 = 0
10t = 0 + -9t
10t = -9t

Solving
10t = -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.
10t + 9t = -9t + 9t

Combine like terms: 10t + 9t = 19t
19t = -9t + 9t

Combine like terms: -9t + 9t = 0
19t = 0

Divide each side by '19'.
t = 0

Simplifying
t = 0