3(t-14)-5(t+12)=0

Solution for 3(t-14)-5(t+12)=0 equation:

Simplifying
3(t + -14) + -5(t + 12) = 0

Reorder the terms:
3(-14 + t) + -5(t + 12) = 0
(-14 * 3 + t * 3) + -5(t + 12) = 0
(-42 + 3t) + -5(t + 12) = 0

Reorder the terms:
-42 + 3t + -5(12 + t) = 0
-42 + 3t + (12 * -5 + t * -5) = 0
-42 + 3t + (-60 + -5t) = 0

Reorder the terms:
-42 + -60 + 3t + -5t = 0

Combine like terms: -42 + -60 = -102
-102 + 3t + -5t = 0

Combine like terms: 3t + -5t = -2t
-102 + -2t = 0

Solving
-102 + -2t = 0

Solving for variable 't'.

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

Add '102' to each side of the equation.
-102 + 102 + -2t = 0 + 102

Combine like terms: -102 + 102 = 0
0 + -2t = 0 + 102
-2t = 0 + 102

Combine like terms: 0 + 102 = 102
-2t = 102

Divide each side by '-2'.
t = -51

Simplifying
t = -51