P(x)=-0.2x^2+8x

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Solution for P(x)=-0.2x^2+8x equation: 


Simplifying
P(x) = -0.2x2 + 8x

Multiply P * x
xP = -0.2x2 + 8x

Reorder the terms:
xP = 8x + -0.2x2

Solving
xP = 8x + -0.2x2

Solving for variable 'x'.

Reorder the terms:
-8x + xP + 0.2x2 = 8x + -0.2x2 + -8x + 0.2x2

Reorder the terms:
-8x + xP + 0.2x2 = 8x + -8x + -0.2x2 + 0.2x2

Combine like terms: 8x + -8x = 0
-8x + xP + 0.2x2 = 0 + -0.2x2 + 0.2x2
-8x + xP + 0.2x2 = -0.2x2 + 0.2x2

Combine like terms: -0.2x2 + 0.2x2 = 0.0
-8x + xP + 0.2x2 = 0.0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + P + 0.2x) = 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 '(-8 + P + 0.2x)' equal to zero and attempt to solve:

Simplifying
-8 + P + 0.2x = 0

Solving
-8 + P + 0.2x = 0

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

Add '8' to each side of the equation.
-8 + P + 8 + 0.2x = 0 + 8

Reorder the terms:
-8 + 8 + P + 0.2x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + P + 0.2x = 0 + 8
P + 0.2x = 0 + 8

Combine like terms: 0 + 8 = 8
P + 0.2x = 8

Add '-1P' to each side of the equation.
P + -1P + 0.2x = 8 + -1P

Combine like terms: P + -1P = 0
0 + 0.2x = 8 + -1P
0.2x = 8 + -1P

Divide each side by '0.2'.
x = 40 + -5P

Simplifying
x = 40 + -5P
Solution
x = {0, 40 + -5P}

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