6*(t-7)=5*(3-t)+2t+6

Solution for 6*(t-7)=5*(3-t)+2t+6 equation:

Simplifying
6(t + -7) = 5(3 + -1t) + 2t + 6

Reorder the terms:
6(-7 + t) = 5(3 + -1t) + 2t + 6
(-7 * 6 + t * 6) = 5(3 + -1t) + 2t + 6
(-42 + 6t) = 5(3 + -1t) + 2t + 6
-42 + 6t = (3 * 5 + -1t * 5) + 2t + 6
-42 + 6t = (15 + -5t) + 2t + 6

Reorder the terms:
-42 + 6t = 15 + 6 + -5t + 2t

Combine like terms: 15 + 6 = 21
-42 + 6t = 21 + -5t + 2t

Combine like terms: -5t + 2t = -3t
-42 + 6t = 21 + -3t

Solving
-42 + 6t = 21 + -3t

Solving for variable 't'.

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

Add '3t' to each side of the equation.
-42 + 6t + 3t = 21 + -3t + 3t

Combine like terms: 6t + 3t = 9t
-42 + 9t = 21 + -3t + 3t

Combine like terms: -3t + 3t = 0
-42 + 9t = 21 + 0
-42 + 9t = 21

Add '42' to each side of the equation.
-42 + 42 + 9t = 21 + 42

Combine like terms: -42 + 42 = 0
0 + 9t = 21 + 42
9t = 21 + 42

Combine like terms: 21 + 42 = 63
9t = 63

Divide each side by '9'.
t = 7

Simplifying
t = 7