(18)(1.8)+(0.5)(1.8)(w-18)=54

Solution for (18)(1.8)+(0.5)(1.8)(w-18)=54 equation:

Simplifying
(18)(1.8) + (0.5)(1.8)(w + -18) = 54

Multiply 18 * 1.8
32.4 + (0.5)(1.8)(w + -18) = 54

Reorder the terms:
32.4 + 0.5 * 1.8(-18 + w) = 54

Multiply 0.5 * 1.8
32.4 + 0.9(-18 + w) = 54
32.4 + (-18 * 0.9 + w * 0.9) = 54
32.4 + (-16.2 + 0.9w) = 54

Combine like terms: 32.4 + -16.2 = 16.2
16.2 + 0.9w = 54

Solving
16.2 + 0.9w = 54

Solving for variable 'w'.

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

Add '-16.2' to each side of the equation.
16.2 + -16.2 + 0.9w = 54 + -16.2

Combine like terms: 16.2 + -16.2 = 0.0
0.0 + 0.9w = 54 + -16.2
0.9w = 54 + -16.2

Combine like terms: 54 + -16.2 = 37.8
0.9w = 37.8

Divide each side by '0.9'.
w = 42

Simplifying
w = 42