(5a+b)-2(3a+4b)=0

Solution for (5a+b)-2(3a+4b)=0 equation:

Simplifying
(5a + b) + -2(3a + 4b) = 0

Remove parenthesis around (5a + b)
5a + b + -2(3a + 4b) = 0
5a + b + (3a * -2 + 4b * -2) = 0
5a + b + (-6a + -8b) = 0

Reorder the terms:
5a + -6a + b + -8b = 0

Combine like terms: 5a + -6a = -1a
-1a + b + -8b = 0

Combine like terms: b + -8b = -7b
-1a + -7b = 0

Solving
-1a + -7b = 0

Solving for variable 'a'.

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

Add '7b' to each side of the equation.
-1a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
-1a + 0 = 0 + 7b
-1a = 0 + 7b
Remove the zero:
-1a = 7b

Divide each side by '-1'.
a = -7b

Simplifying
a = -7b