F(x)=.04(8x-x^2)

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Solution for F(x)=.04(8x-x^2) equation: 


Simplifying
F(x) = 0.04(8x + -1x2)

Multiply F * x
xF = 0.04(8x + -1x2)
xF = (8x * 0.04 + -1x2 * 0.04)
xF = (0.32x + -0.04x2)

Solving
xF = 0.32x + -0.04x2

Solving for variable 'x'.

Reorder the terms:
-0.32x + xF + 0.04x2 = 0.32x + -0.04x2 + -0.32x + 0.04x2

Reorder the terms:
-0.32x + xF + 0.04x2 = 0.32x + -0.32x + -0.04x2 + 0.04x2

Combine like terms: 0.32x + -0.32x = 0.00
-0.32x + xF + 0.04x2 = 0.00 + -0.04x2 + 0.04x2
-0.32x + xF + 0.04x2 = -0.04x2 + 0.04x2

Combine like terms: -0.04x2 + 0.04x2 = 0.00
-0.32x + xF + 0.04x2 = 0.00

Factor out the Greatest Common Factor (GCF), 'x'.
x(-0.32 + F + 0.04x) = 0.00


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 '(-0.32 + F + 0.04x)' equal to zero and attempt to solve:

Simplifying
-0.32 + F + 0.04x = 0

Solving
-0.32 + F + 0.04x = 0

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

Add '0.32' to each side of the equation.
-0.32 + F + 0.32 + 0.04x = 0 + 0.32

Reorder the terms:
-0.32 + 0.32 + F + 0.04x = 0 + 0.32

Combine like terms: -0.32 + 0.32 = 0.00
0.00 + F + 0.04x = 0 + 0.32
F + 0.04x = 0 + 0.32

Combine like terms: 0 + 0.32 = 0.32
F + 0.04x = 0.32

Add '-1F' to each side of the equation.
F + -1F + 0.04x = 0.32 + -1F

Combine like terms: F + -1F = 0
0 + 0.04x = 0.32 + -1F
0.04x = 0.32 + -1F

Divide each side by '0.04'.
x = 8 + -25F

Simplifying
x = 8 + -25F
Solution
x = {0, 8 + -25F}

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