45.5+0.15(10k)=90.5

Solution for 45.5+0.15(10k)=90.5 equation:

Simplifying
45.5 + 0.15(10k) = 90.5

Remove parenthesis around (10k)
45.5 + 0.15 * 10k = 90.5

Multiply 0.15 * 10
45.5 + 1.5k = 90.5

Solving
45.5 + 1.5k = 90.5

Solving for variable 'k'.

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

Add '-45.5' to each side of the equation.
45.5 + -45.5 + 1.5k = 90.5 + -45.5

Combine like terms: 45.5 + -45.5 = 0.0
0.0 + 1.5k = 90.5 + -45.5
1.5k = 90.5 + -45.5

Combine like terms: 90.5 + -45.5 = 45
1.5k = 45

Divide each side by '1.5'.
k = 30

Simplifying
k = 30