f(x)=a(x+2)(x-1)(x-3)

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Solution for f(x)=a(x+2)(x-1)(x-3) equation:


Simplifying
f(x) = a(x + 2)(x + -1)(x + -3)

Multiply f * x
fx = a(x + 2)(x + -1)(x + -3)

Reorder the terms:
fx = a(2 + x)(x + -1)(x + -3)

Reorder the terms:
fx = a(2 + x)(-1 + x)(x + -3)

Reorder the terms:
fx = a(2 + x)(-1 + x)(-3 + x)

Multiply (2 + x) * (-1 + x)
fx = a(2(-1 + x) + x(-1 + x))(-3 + x)
fx = a((-1 * 2 + x * 2) + x(-1 + x))(-3 + x)
fx = a((-2 + 2x) + x(-1 + x))(-3 + x)
fx = a(-2 + 2x + (-1 * x + x * x))(-3 + x)
fx = a(-2 + 2x + (-1x + x2))(-3 + x)

Combine like terms: 2x + -1x = 1x
fx = a(-2 + 1x + x2)(-3 + x)

Multiply (-2 + 1x + x2) * (-3 + x)
fx = a(-2(-3 + x) + 1x * (-3 + x) + x2(-3 + x))
fx = a((-3 * -2 + x * -2) + 1x * (-3 + x) + x2(-3 + x))
fx = a((6 + -2x) + 1x * (-3 + x) + x2(-3 + x))
fx = a(6 + -2x + (-3 * 1x + x * 1x) + x2(-3 + x))
fx = a(6 + -2x + (-3x + 1x2) + x2(-3 + x))
fx = a(6 + -2x + -3x + 1x2 + (-3 * x2 + x * x2))
fx = a(6 + -2x + -3x + 1x2 + (-3x2 + x3))

Combine like terms: -2x + -3x = -5x
fx = a(6 + -5x + 1x2 + -3x2 + x3)

Combine like terms: 1x2 + -3x2 = -2x2
fx = a(6 + -5x + -2x2 + x3)
fx = (6 * a + -5x * a + -2x2 * a + x3 * a)
fx = (6a + -5ax + -2ax2 + ax3)

Solving
fx = 6a + -5ax + -2ax2 + ax3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 6ax-1 + -5a + -2ax + ax2

Simplifying
f = 6ax-1 + -5a + -2ax + ax2

Reorder the terms:
f = -5a + 6ax-1 + -2ax + ax2

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