6(t-7)+8(-5t-8)=-35(3+t)-8

Solution for 6(t-7)+8(-5t-8)=-35(3+t)-8 equation:

Simplifying
6(t + -7) + 8(-5t + -8) = -35(3 + t) + -8

Reorder the terms:
6(-7 + t) + 8(-5t + -8) = -35(3 + t) + -8
(-7 * 6 + t * 6) + 8(-5t + -8) = -35(3 + t) + -8
(-42 + 6t) + 8(-5t + -8) = -35(3 + t) + -8

Reorder the terms:
-42 + 6t + 8(-8 + -5t) = -35(3 + t) + -8
-42 + 6t + (-8 * 8 + -5t * 8) = -35(3 + t) + -8
-42 + 6t + (-64 + -40t) = -35(3 + t) + -8

Reorder the terms:
-42 + -64 + 6t + -40t = -35(3 + t) + -8

Combine like terms: -42 + -64 = -106
-106 + 6t + -40t = -35(3 + t) + -8

Combine like terms: 6t + -40t = -34t
-106 + -34t = -35(3 + t) + -8
-106 + -34t = (3 * -35 + t * -35) + -8
-106 + -34t = (-105 + -35t) + -8

Reorder the terms:
-106 + -34t = -105 + -8 + -35t

Combine like terms: -105 + -8 = -113
-106 + -34t = -113 + -35t

Solving
-106 + -34t = -113 + -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.
-106 + -34t + 35t = -113 + -35t + 35t

Combine like terms: -34t + 35t = 1t
-106 + 1t = -113 + -35t + 35t

Combine like terms: -35t + 35t = 0
-106 + 1t = -113 + 0
-106 + 1t = -113

Add '106' to each side of the equation.
-106 + 106 + 1t = -113 + 106

Combine like terms: -106 + 106 = 0
0 + 1t = -113 + 106
1t = -113 + 106

Combine like terms: -113 + 106 = -7
1t = -7

Divide each side by '1'.
t = -7

Simplifying
t = -7