R(x)=x(100-0.4x)

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Solution for R(x)=x(100-0.4x) equation: 


Simplifying
R(x) = x(100 + -0.4x)

Multiply R * x
xR = x(100 + -0.4x)
xR = (100 * x + -0.4x * x)
xR = (100x + -0.4x2)

Solving
xR = 100x + -0.4x2

Solving for variable 'x'.

Reorder the terms:
-100x + xR + 0.4x2 = 100x + -0.4x2 + -100x + 0.4x2

Reorder the terms:
-100x + xR + 0.4x2 = 100x + -100x + -0.4x2 + 0.4x2

Combine like terms: 100x + -100x = 0
-100x + xR + 0.4x2 = 0 + -0.4x2 + 0.4x2
-100x + xR + 0.4x2 = -0.4x2 + 0.4x2

Combine like terms: -0.4x2 + 0.4x2 = 0.0
-100x + xR + 0.4x2 = 0.0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-100 + R + 0.4x) = 0.0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-100 + R + 0.4x)' equal to zero and attempt to solve:

Simplifying
-100 + R + 0.4x = 0

Solving
-100 + R + 0.4x = 0

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

Add '100' to each side of the equation.
-100 + R + 100 + 0.4x = 0 + 100

Reorder the terms:
-100 + 100 + R + 0.4x = 0 + 100

Combine like terms: -100 + 100 = 0
0 + R + 0.4x = 0 + 100
R + 0.4x = 0 + 100

Combine like terms: 0 + 100 = 100
R + 0.4x = 100

Add '-1R' to each side of the equation.
R + -1R + 0.4x = 100 + -1R

Combine like terms: R + -1R = 0
0 + 0.4x = 100 + -1R
0.4x = 100 + -1R

Divide each side by '0.4'.
x = 250 + -2.5R

Simplifying
x = 250 + -2.5R
Solution
x = {0, 250 + -2.5R}

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