42=6(5+2r)+4(1-5r)

Solution for 42=6(5+2r)+4(1-5r) equation:

Simplifying
42 = 6(5 + 2r) + 4(1 + -5r)
42 = (5 * 6 + 2r * 6) + 4(1 + -5r)
42 = (30 + 12r) + 4(1 + -5r)
42 = 30 + 12r + (1 * 4 + -5r * 4)
42 = 30 + 12r + (4 + -20r)

Reorder the terms:
42 = 30 + 4 + 12r + -20r

Combine like terms: 30 + 4 = 34
42 = 34 + 12r + -20r

Combine like terms: 12r + -20r = -8r
42 = 34 + -8r

Solving
42 = 34 + -8r

Solving for variable 'r'.

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

Add '8r' to each side of the equation.
42 + 8r = 34 + -8r + 8r

Combine like terms: -8r + 8r = 0
42 + 8r = 34 + 0
42 + 8r = 34

Add '-42' to each side of the equation.
42 + -42 + 8r = 34 + -42

Combine like terms: 42 + -42 = 0
0 + 8r = 34 + -42
8r = 34 + -42

Combine like terms: 34 + -42 = -8
8r = -8

Divide each side by '8'.
r = -1

Simplifying
r = -1