100*(1.03)*(1.06)*(1+(x-0.5))=100

Solution for 100*(1.03)*(1.06)*(1+(x-0.5))=100 equation:

Simplifying
100(1.03)(1.06)(1 + (x + -0.5)) = 100

Reorder the terms:
100 * 1.03 * 1.06(1 + (-0.5 + x)) = 100

Remove parenthesis around (-0.5 + x)
100 * 1.03 * 1.06(1 + -0.5 + x) = 100

Combine like terms: 1 + -0.5 = 0.5
100 * 1.03 * 1.06(0.5 + x) = 100

Multiply 100 * 1.03
103 * 1.06(0.5 + x) = 100

Multiply 103 * 1.06
109.18(0.5 + x) = 100
(0.5 * 109.18 + x * 109.18) = 100
(54.59 + 109.18x) = 100

Solving
54.59 + 109.18x = 100

Solving for variable 'x'.

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

Add '-54.59' to each side of the equation.
54.59 + -54.59 + 109.18x = 100 + -54.59

Combine like terms: 54.59 + -54.59 = 0.00
0.00 + 109.18x = 100 + -54.59
109.18x = 100 + -54.59

Combine like terms: 100 + -54.59 = 45.41
109.18x = 45.41

Divide each side by '109.18'.
x = 0.4159186664

Simplifying
x = 0.4159186664