R(x)=x(90-4x)

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Solution for R(x)=x(90-4x) equation: 


Simplifying
R(x) = x(90 + -4x)

Multiply R * x
xR = x(90 + -4x)
xR = (90 * x + -4x * x)
xR = (90x + -4x2)

Solving
xR = 90x + -4x2

Solving for variable 'x'.

Reorder the terms:
-90x + xR + 4x2 = 90x + -4x2 + -90x + 4x2

Reorder the terms:
-90x + xR + 4x2 = 90x + -90x + -4x2 + 4x2

Combine like terms: 90x + -90x = 0
-90x + xR + 4x2 = 0 + -4x2 + 4x2
-90x + xR + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-90x + xR + 4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-90 + R + 4x) = 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 '(-90 + R + 4x)' equal to zero and attempt to solve:

Simplifying
-90 + R + 4x = 0

Solving
-90 + R + 4x = 0

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

Add '90' to each side of the equation.
-90 + R + 90 + 4x = 0 + 90

Reorder the terms:
-90 + 90 + R + 4x = 0 + 90

Combine like terms: -90 + 90 = 0
0 + R + 4x = 0 + 90
R + 4x = 0 + 90

Combine like terms: 0 + 90 = 90
R + 4x = 90

Add '-1R' to each side of the equation.
R + -1R + 4x = 90 + -1R

Combine like terms: R + -1R = 0
0 + 4x = 90 + -1R
4x = 90 + -1R

Divide each side by '4'.
x = 22.5 + -0.25R

Simplifying
x = 22.5 + -0.25R
Solution
x = {0, 22.5 + -0.25R}

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