2(t-3)-3(t-2)=t+8

Solution for 2(t-3)-3(t-2)=t+8 equation:

Simplifying
2(t + -3) + -3(t + -2) = t + 8

Reorder the terms:
2(-3 + t) + -3(t + -2) = t + 8
(-3 * 2 + t * 2) + -3(t + -2) = t + 8
(-6 + 2t) + -3(t + -2) = t + 8

Reorder the terms:
-6 + 2t + -3(-2 + t) = t + 8
-6 + 2t + (-2 * -3 + t * -3) = t + 8
-6 + 2t + (6 + -3t) = t + 8

Reorder the terms:
-6 + 6 + 2t + -3t = t + 8

Combine like terms: -6 + 6 = 0
0 + 2t + -3t = t + 8
2t + -3t = t + 8

Combine like terms: 2t + -3t = -1t
-1t = t + 8

Reorder the terms:
-1t = 8 + t

Solving
-1t = 8 + t

Solving for variable 't'.

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

Add '-1t' to each side of the equation.
-1t + -1t = 8 + t + -1t

Combine like terms: -1t + -1t = -2t
-2t = 8 + t + -1t

Combine like terms: t + -1t = 0
-2t = 8 + 0
-2t = 8

Divide each side by '-2'.
t = -4

Simplifying
t = -4