a*(2*c*x)+b*(2*d*x)=42

Solution for a*(2*c*x)+b*(2*d*x)=42 equation:

Simplifying
a(2c * x) + b(2d * x) = 42

Multiply c * x
a(2cx) + b(2d * x) = 42

Remove parenthesis around (2cx)
a * 2cx + b(2d * x) = 42

Reorder the terms for easier multiplication:
2a * cx + b(2d * x) = 42

Multiply a * cx
2acx + b(2d * x) = 42

Multiply d * x
2acx + b(2dx) = 42

Remove parenthesis around (2dx)
2acx + b * 2dx = 42

Reorder the terms for easier multiplication:
2acx + 2b * dx = 42

Multiply b * dx
2acx + 2bdx = 42

Solving
2acx + 2bdx = 42

Solving for variable 'a'.

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

Add '-2bdx' to each side of the equation.
2acx + 2bdx + -2bdx = 42 + -2bdx

Combine like terms: 2bdx + -2bdx = 0
2acx + 0 = 42 + -2bdx
2acx = 42 + -2bdx

Divide each side by '2cx'.
a = 21c-1x-1 + -1bc-1d

Simplifying
a = 21c-1x-1 + -1bc-1d

Reorder the terms:
a = -1bc-1d + 21c-1x-1