(x-a)(x-b)=abx^2

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


Simplifying
(x + -1a)(x + -1b) = abx2

Reorder the terms:
(-1a + x)(x + -1b) = abx2

Reorder the terms:
(-1a + x)(-1b + x) = abx2

Multiply (-1a + x) * (-1b + x)
(-1a * (-1b + x) + x(-1b + x)) = abx2
((-1b * -1a + x * -1a) + x(-1b + x)) = abx2
((1ab + -1ax) + x(-1b + x)) = abx2
(1ab + -1ax + (-1b * x + x * x)) = abx2
(1ab + -1ax + (-1bx + x2)) = abx2
(1ab + -1ax + -1bx + x2) = abx2

Solving
1ab + -1ax + -1bx + x2 = abx2

Solving for variable 'a'.

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

Add '-1abx2' to each side of the equation.
1ab + -1ax + -1bx + -1abx2 + x2 = abx2 + -1abx2

Reorder the terms:
1ab + -1abx2 + -1ax + -1bx + x2 = abx2 + -1abx2

Combine like terms: abx2 + -1abx2 = 0
1ab + -1abx2 + -1ax + -1bx + x2 = 0

Add 'bx' to each side of the equation.
1ab + -1abx2 + -1ax + -1bx + bx + x2 = 0 + bx

Combine like terms: -1bx + bx = 0
1ab + -1abx2 + -1ax + 0 + x2 = 0 + bx
1ab + -1abx2 + -1ax + x2 = 0 + bx
Remove the zero:
1ab + -1abx2 + -1ax + x2 = bx

Add '-1x2' to each side of the equation.
1ab + -1abx2 + -1ax + x2 + -1x2 = bx + -1x2

Combine like terms: x2 + -1x2 = 0
1ab + -1abx2 + -1ax + 0 = bx + -1x2
1ab + -1abx2 + -1ax = bx + -1x2

Reorder the terms:
1ab + -1abx2 + -1ax + -1bx + x2 = bx + -1bx + -1x2 + x2

Combine like terms: bx + -1bx = 0
1ab + -1abx2 + -1ax + -1bx + x2 = 0 + -1x2 + x2
1ab + -1abx2 + -1ax + -1bx + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
1ab + -1abx2 + -1ax + -1bx + x2 = 0

The solution to this equation could not be determined.

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