f(x)=k(x-a)(x-b)

Solution for f(x)=k(x-a)(x-b) equation:

Simplifying
f(x) = k(x + -1a)(x + -1b)

Multiply f * x
fx = k(x + -1a)(x + -1b)

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

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

Multiply (-1a + x) * (-1b + x)
fx = k(-1a * (-1b + x) + x(-1b + x))
fx = k((-1b * -1a + x * -1a) + x(-1b + x))
fx = k((1ab + -1ax) + x(-1b + x))
fx = k(1ab + -1ax + (-1b * x + x * x))
fx = k(1ab + -1ax + (-1bx + x2))
fx = k(1ab + -1ax + -1bx + x2)
fx = (1ab * k + -1ax * k + -1bx * k + x2 * k)
fx = (1abk + -1akx + -1bkx + kx2)

Solving
fx = 1abk + -1akx + -1bkx + kx2

Solving for variable 'f'.

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

Divide each side by 'x'.
f = abkx-1 + -1ak + -1bk + kx

Simplifying
f = abkx-1 + -1ak + -1bk + kx