R(x)=x(75-3x)

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Solution for R(x)=x(75-3x) equation: 


Simplifying
R(x) = x(75 + -3x)

Multiply R * x
xR = x(75 + -3x)
xR = (75 * x + -3x * x)
xR = (75x + -3x2)

Solving
xR = 75x + -3x2

Solving for variable 'x'.

Reorder the terms:
-75x + xR + 3x2 = 75x + -3x2 + -75x + 3x2

Reorder the terms:
-75x + xR + 3x2 = 75x + -75x + -3x2 + 3x2

Combine like terms: 75x + -75x = 0
-75x + xR + 3x2 = 0 + -3x2 + 3x2
-75x + xR + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-75x + xR + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-75 + R + 3x) = 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 '(-75 + R + 3x)' equal to zero and attempt to solve:

Simplifying
-75 + R + 3x = 0

Solving
-75 + R + 3x = 0

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

Add '75' to each side of the equation.
-75 + R + 75 + 3x = 0 + 75

Reorder the terms:
-75 + 75 + R + 3x = 0 + 75

Combine like terms: -75 + 75 = 0
0 + R + 3x = 0 + 75
R + 3x = 0 + 75

Combine like terms: 0 + 75 = 75
R + 3x = 75

Add '-1R' to each side of the equation.
R + -1R + 3x = 75 + -1R

Combine like terms: R + -1R = 0
0 + 3x = 75 + -1R
3x = 75 + -1R

Divide each side by '3'.
x = 25 + -0.3333333333R

Simplifying
x = 25 + -0.3333333333R
Solution
x = {0, 25 + -0.3333333333R}

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