3(t+3)-3(5t+1)=-13(t+1)+2

Solution for 3(t+3)-3(5t+1)=-13(t+1)+2 equation:

Simplifying
3(t + 3) + -3(5t + 1) = -13(t + 1) + 2

Reorder the terms:
3(3 + t) + -3(5t + 1) = -13(t + 1) + 2
(3 * 3 + t * 3) + -3(5t + 1) = -13(t + 1) + 2
(9 + 3t) + -3(5t + 1) = -13(t + 1) + 2

Reorder the terms:
9 + 3t + -3(1 + 5t) = -13(t + 1) + 2
9 + 3t + (1 * -3 + 5t * -3) = -13(t + 1) + 2
9 + 3t + (-3 + -15t) = -13(t + 1) + 2

Reorder the terms:
9 + -3 + 3t + -15t = -13(t + 1) + 2

Combine like terms: 9 + -3 = 6
6 + 3t + -15t = -13(t + 1) + 2

Combine like terms: 3t + -15t = -12t
6 + -12t = -13(t + 1) + 2

Reorder the terms:
6 + -12t = -13(1 + t) + 2
6 + -12t = (1 * -13 + t * -13) + 2
6 + -12t = (-13 + -13t) + 2

Reorder the terms:
6 + -12t = -13 + 2 + -13t

Combine like terms: -13 + 2 = -11
6 + -12t = -11 + -13t

Solving
6 + -12t = -11 + -13t

Solving for variable 't'.

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

Add '13t' to each side of the equation.
6 + -12t + 13t = -11 + -13t + 13t

Combine like terms: -12t + 13t = 1t
6 + 1t = -11 + -13t + 13t

Combine like terms: -13t + 13t = 0
6 + 1t = -11 + 0
6 + 1t = -11

Add '-6' to each side of the equation.
6 + -6 + 1t = -11 + -6

Combine like terms: 6 + -6 = 0
0 + 1t = -11 + -6
1t = -11 + -6

Combine like terms: -11 + -6 = -17
1t = -17

Divide each side by '1'.
t = -17

Simplifying
t = -17