2(t-3)-3(4t-3)=4-7(5t+1)

Solution for 2(t-3)-3(4t-3)=4-7(5t+1) equation:

Simplifying
2(t + -3) + -3(4t + -3) = 4 + -7(5t + 1)

Reorder the terms:
2(-3 + t) + -3(4t + -3) = 4 + -7(5t + 1)
(-3 * 2 + t * 2) + -3(4t + -3) = 4 + -7(5t + 1)
(-6 + 2t) + -3(4t + -3) = 4 + -7(5t + 1)

Reorder the terms:
-6 + 2t + -3(-3 + 4t) = 4 + -7(5t + 1)
-6 + 2t + (-3 * -3 + 4t * -3) = 4 + -7(5t + 1)
-6 + 2t + (9 + -12t) = 4 + -7(5t + 1)

Reorder the terms:
-6 + 9 + 2t + -12t = 4 + -7(5t + 1)

Combine like terms: -6 + 9 = 3
3 + 2t + -12t = 4 + -7(5t + 1)

Combine like terms: 2t + -12t = -10t
3 + -10t = 4 + -7(5t + 1)

Reorder the terms:
3 + -10t = 4 + -7(1 + 5t)
3 + -10t = 4 + (1 * -7 + 5t * -7)
3 + -10t = 4 + (-7 + -35t)

Combine like terms: 4 + -7 = -3
3 + -10t = -3 + -35t

Solving
3 + -10t = -3 + -35t

Solving for variable 't'.

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

Add '35t' to each side of the equation.
3 + -10t + 35t = -3 + -35t + 35t

Combine like terms: -10t + 35t = 25t
3 + 25t = -3 + -35t + 35t

Combine like terms: -35t + 35t = 0
3 + 25t = -3 + 0
3 + 25t = -3

Add '-3' to each side of the equation.
3 + -3 + 25t = -3 + -3

Combine like terms: 3 + -3 = 0
0 + 25t = -3 + -3
25t = -3 + -3

Combine like terms: -3 + -3 = -6
25t = -6

Divide each side by '25'.
t = -0.24

Simplifying
t = -0.24