.15=w*.12+(1-w)*.20

Solution for .15=w*.12+(1-w)*.20 equation:

Simplifying
0.15 = w * 0.12 + (1 + -1w) * 0.20

Reorder the terms for easier multiplication:
0.15 = 0.12w + (1 + -1w) * 0.20

Reorder the terms for easier multiplication:
0.15 = 0.12w + 0.20(1 + -1w)
0.15 = 0.12w + (1 * 0.20 + -1w * 0.20)
0.15 = 0.12w + (0.2 + -0.2w)

Reorder the terms:
0.15 = 0.2 + 0.12w + -0.2w

Combine like terms: 0.12w + -0.2w = -0.08w
0.15 = 0.2 + -0.08w

Solving
0.15 = 0.2 + -0.08w

Solving for variable 'w'.

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

Add '0.08w' to each side of the equation.
0.15 + 0.08w = 0.2 + -0.08w + 0.08w

Combine like terms: -0.08w + 0.08w = 0.00
0.15 + 0.08w = 0.2 + 0.00
0.15 + 0.08w = 0.2

Add '-0.15' to each side of the equation.
0.15 + -0.15 + 0.08w = 0.2 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + 0.08w = 0.2 + -0.15
0.08w = 0.2 + -0.15

Combine like terms: 0.2 + -0.15 = 0.05
0.08w = 0.05

Divide each side by '0.08'.
w = 0.625

Simplifying
w = 0.625