F(x)=(b-2x)(a-2x)x

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Solution for F(x)=(b-2x)(a-2x)x equation: 


Simplifying
F(x) = (b + -2x)(a + -2x) * x

Multiply F * x
xF = (b + -2x)(a + -2x) * x

Reorder the terms for easier multiplication:
xF = x(b + -2x)(a + -2x)

Multiply (b + -2x) * (a + -2x)
xF = x(b(a + -2x) + -2x * (a + -2x))
xF = x((a * b + -2x * b) + -2x * (a + -2x))
xF = x((ab + -2bx) + -2x * (a + -2x))
xF = x(ab + -2bx + (a * -2x + -2x * -2x))
xF = x(ab + -2bx + (-2ax + 4x2))

Reorder the terms:
xF = x(ab + -2ax + -2bx + 4x2)
xF = x(ab + -2ax + -2bx + 4x2)
xF = (ab * x + -2ax * x + -2bx * x + 4x2 * x)
xF = (abx + -2ax2 + -2bx2 + 4x3)

Solving
xF = abx + -2ax2 + -2bx2 + 4x3

Solving for variable 'x'.

Reorder the terms:
-1abx + 2ax2 + 2bx2 + xF + -4x3 = abx + -2ax2 + -2bx2 + 4x3 + -1abx + 2ax2 + 2bx2 + -4x3

Reorder the terms:
-1abx + 2ax2 + 2bx2 + xF + -4x3 = abx + -1abx + -2ax2 + 2ax2 + -2bx2 + 2bx2 + 4x3 + -4x3

Combine like terms: abx + -1abx = 0
-1abx + 2ax2 + 2bx2 + xF + -4x3 = 0 + -2ax2 + 2ax2 + -2bx2 + 2bx2 + 4x3 + -4x3
-1abx + 2ax2 + 2bx2 + xF + -4x3 = -2ax2 + 2ax2 + -2bx2 + 2bx2 + 4x3 + -4x3

Combine like terms: -2ax2 + 2ax2 = 0
-1abx + 2ax2 + 2bx2 + xF + -4x3 = 0 + -2bx2 + 2bx2 + 4x3 + -4x3
-1abx + 2ax2 + 2bx2 + xF + -4x3 = -2bx2 + 2bx2 + 4x3 + -4x3

Combine like terms: -2bx2 + 2bx2 = 0
-1abx + 2ax2 + 2bx2 + xF + -4x3 = 0 + 4x3 + -4x3
-1abx + 2ax2 + 2bx2 + xF + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-1abx + 2ax2 + 2bx2 + xF + -4x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1ab + 2ax + 2bx + F + -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 '(-1ab + 2ax + 2bx + F + -4x2)' equal to zero and attempt to solve:

Simplifying
-1ab + 2ax + 2bx + F + -4x2 = 0

Reorder the terms:
F + -1ab + 2ax + 2bx + -4x2 = 0

Solving
F + -1ab + 2ax + 2bx + -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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