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

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

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

Reorder the terms:
2(-3 + t) + -3(2t + -3) = 3 + -5(3t + 1)
(-3 * 2 + t * 2) + -3(2t + -3) = 3 + -5(3t + 1)
(-6 + 2t) + -3(2t + -3) = 3 + -5(3t + 1)

Reorder the terms:
-6 + 2t + -3(-3 + 2t) = 3 + -5(3t + 1)
-6 + 2t + (-3 * -3 + 2t * -3) = 3 + -5(3t + 1)
-6 + 2t + (9 + -6t) = 3 + -5(3t + 1)

Reorder the terms:
-6 + 9 + 2t + -6t = 3 + -5(3t + 1)

Combine like terms: -6 + 9 = 3
3 + 2t + -6t = 3 + -5(3t + 1)

Combine like terms: 2t + -6t = -4t
3 + -4t = 3 + -5(3t + 1)

Reorder the terms:
3 + -4t = 3 + -5(1 + 3t)
3 + -4t = 3 + (1 * -5 + 3t * -5)
3 + -4t = 3 + (-5 + -15t)

Combine like terms: 3 + -5 = -2
3 + -4t = -2 + -15t

Solving
3 + -4t = -2 + -15t

Solving for variable 't'.

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

Add '15t' to each side of the equation.
3 + -4t + 15t = -2 + -15t + 15t

Combine like terms: -4t + 15t = 11t
3 + 11t = -2 + -15t + 15t

Combine like terms: -15t + 15t = 0
3 + 11t = -2 + 0
3 + 11t = -2

Add '-3' to each side of the equation.
3 + -3 + 11t = -2 + -3

Combine like terms: 3 + -3 = 0
0 + 11t = -2 + -3
11t = -2 + -3

Combine like terms: -2 + -3 = -5
11t = -5

Divide each side by '11'.
t = -0.4545454545

Simplifying
t = -0.4545454545