r(x)=(1+0.05x)(4000-80x)

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Solution for r(x)=(1+0.05x)(4000-80x) equation: 


Simplifying
r(x) = (1 + 0.05x)(4000 + -80x)

Multiply r * x
rx = (1 + 0.05x)(4000 + -80x)

Multiply (1 + 0.05x) * (4000 + -80x)
rx = (1(4000 + -80x) + 0.05x * (4000 + -80x))
rx = ((4000 * 1 + -80x * 1) + 0.05x * (4000 + -80x))
rx = ((4000 + -80x) + 0.05x * (4000 + -80x))
rx = (4000 + -80x + (4000 * 0.05x + -80x * 0.05x))
rx = (4000 + -80x + (200x + -4x2))

Combine like terms: -80x + 200x = 120x
rx = (4000 + 120x + -4x2)

Solving
rx = 4000 + 120x + -4x2

Solving for variable 'r'.

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

Divide each side by 'x'.
r = 4000x-1 + 120 + -4x

Simplifying
r = 4000x-1 + 120 + -4x

Reorder the terms:
r = 120 + 4000x-1 + -4x

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