V(x)=x(10-2x)(10-2x)

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Solution for V(x)=x(10-2x)(10-2x) equation: 


Simplifying
V(x) = x(10 + -2x)(10 + -2x)

Multiply V * x
xV = x(10 + -2x)(10 + -2x)

Multiply (10 + -2x) * (10 + -2x)
xV = x(10(10 + -2x) + -2x * (10 + -2x))
xV = x((10 * 10 + -2x * 10) + -2x * (10 + -2x))
xV = x((100 + -20x) + -2x * (10 + -2x))
xV = x(100 + -20x + (10 * -2x + -2x * -2x))
xV = x(100 + -20x + (-20x + 4x2))

Combine like terms: -20x + -20x = -40x
xV = x(100 + -40x + 4x2)
xV = (100 * x + -40x * x + 4x2 * x)
xV = (100x + -40x2 + 4x3)

Solving
xV = 100x + -40x2 + 4x3

Solving for variable 'x'.

Reorder the terms:
-100x + xV + 40x2 + -4x3 = 100x + -40x2 + 4x3 + -100x + 40x2 + -4x3

Reorder the terms:
-100x + xV + 40x2 + -4x3 = 100x + -100x + -40x2 + 40x2 + 4x3 + -4x3

Combine like terms: 100x + -100x = 0
-100x + xV + 40x2 + -4x3 = 0 + -40x2 + 40x2 + 4x3 + -4x3
-100x + xV + 40x2 + -4x3 = -40x2 + 40x2 + 4x3 + -4x3

Combine like terms: -40x2 + 40x2 = 0
-100x + xV + 40x2 + -4x3 = 0 + 4x3 + -4x3
-100x + xV + 40x2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-100x + xV + 40x2 + -4x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-100 + V + 40x + -4x2) = 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 + V + 40x + -4x2)' equal to zero and attempt to solve:

Simplifying
-100 + V + 40x + -4x2 = 0

Solving
-100 + V + 40x + -4x2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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