(r*5)+(1*2)=(2*6)+(3*4)+(4*2)

Solution for (r*5)+(1*2)=(2*6)+(3*4)+(4*2) equation:

Simplifying
(r * 5) + (1 * 2) = (2 * 6) + (3 * 4) + (4 * 2)

Reorder the terms for easier multiplication:
(5r) + (1 * 2) = (2 * 6) + (3 * 4) + (4 * 2)

Multiply 1 * 2
(5r) + (2) = (2 * 6) + (3 * 4) + (4 * 2)
(5r) + 2 = (2 * 6) + (3 * 4) + (4 * 2)

Reorder the terms:
2 + (5r) = (2 * 6) + (3 * 4) + (4 * 2)

Multiply 2 * 6
2 + (5r) = (12) + (3 * 4) + (4 * 2)
2 + (5r) = 12 + (3 * 4) + (4 * 2)

Multiply 3 * 4
2 + (5r) = 12 + (12) + (4 * 2)
2 + (5r) = 12 + 12 + (4 * 2)

Multiply 4 * 2
2 + (5r) = 12 + 12 + (8)
2 + (5r) = 12 + 12 + 8

Combine like terms: 12 + 12 = 24
2 + (5r) = 24 + 8

Combine like terms: 24 + 8 = 32
2 + (5r) = 32

Solving
2 + (5r) = 32

Solving for variable 'r'.

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

Add '-2' to each side of the equation.
2 + -2 + (5r) = 32 + -2

Combine like terms: 2 + -2 = 0
0 + (5r) = 32 + -2
(5r) = 32 + -2

Combine like terms: 32 + -2 = 30
(5r) = 30

Divide each side by '5'.
r = 6

Simplifying
r = 6