x(a-2x)(b-2x)=0

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Solution for x(a-2x)(b-2x)=0 equation: 


Simplifying
x(a + -2x)(b + -2x) = 0

Multiply (a + -2x) * (b + -2x)
x(a(b + -2x) + -2x * (b + -2x)) = 0
x((b * a + -2x * a) + -2x * (b + -2x)) = 0
x((ab + -2ax) + -2x * (b + -2x)) = 0
x(ab + -2ax + (b * -2x + -2x * -2x)) = 0
x(ab + -2ax + (-2bx + 4x2)) = 0
x(ab + -2ax + -2bx + 4x2) = 0
(ab * x + -2ax * x + -2bx * x + 4x2 * x) = 0
(abx + -2ax2 + -2bx2 + 4x3) = 0

Solving
abx + -2ax2 + -2bx2 + 4x3 = 0

Solving for variable 'a'.

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

Add '2bx2' to each side of the equation.
abx + -2ax2 + -2bx2 + 2bx2 + 4x3 = 0 + 2bx2

Combine like terms: -2bx2 + 2bx2 = 0
abx + -2ax2 + 0 + 4x3 = 0 + 2bx2
abx + -2ax2 + 4x3 = 0 + 2bx2
Remove the zero:
abx + -2ax2 + 4x3 = 2bx2

Add '-4x3' to each side of the equation.
abx + -2ax2 + 4x3 + -4x3 = 2bx2 + -4x3

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(ab + -2ax + -2bx + 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 a to the left, all other terms to the right.

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(ab + -2ax + -2bx + 4x2)' equal to zero and attempt to solve:

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

Solving
ab + -2ax + -2bx + 4x2 = 0

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

Add '2bx' to each side of the equation.
ab + -2ax + -2bx + 2bx + 4x2 = 0 + 2bx

Combine like terms: -2bx + 2bx = 0
ab + -2ax + 0 + 4x2 = 0 + 2bx
ab + -2ax + 4x2 = 0 + 2bx
Remove the zero:
ab + -2ax + 4x2 = 2bx

Add '-4x2' to each side of the equation.
ab + -2ax + 4x2 + -4x2 = 2bx + -4x2

Combine like terms: 4x2 + -4x2 = 0
ab + -2ax + 0 = 2bx + -4x2
ab + -2ax = 2bx + -4x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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