f(X)=5x(X-1)(x+1)+5x

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Solution for f(X)=5x(X-1)(x+1)+5x equation:


Simplifying
f(X) = 5x(X + -1)(x + 1) + 5x

Multiply f * X
fX = 5x(X + -1)(x + 1) + 5x

Reorder the terms:
fX = 5x(-1 + X)(x + 1) + 5x

Reorder the terms:
fX = 5x(-1 + X)(1 + x) + 5x

Multiply (-1 + X) * (1 + x)
fX = 5x(-1(1 + x) + X(1 + x)) + 5x
fX = 5x((1 * -1 + x * -1) + X(1 + x)) + 5x
fX = 5x((-1 + -1x) + X(1 + x)) + 5x
fX = 5x(-1 + -1x + (1 * X + x * X)) + 5x
fX = 5x(-1 + -1x + (1X + xX)) + 5x

Reorder the terms:
fX = 5x(-1 + 1X + -1x + xX) + 5x
fX = 5x(-1 + 1X + -1x + xX) + 5x
fX = (-1 * 5x + 1X * 5x + -1x * 5x + xX * 5x) + 5x
fX = (-5x + 5xX + -5x2 + 5x2X) + 5x

Reorder the terms:
fX = -5x + 5x + 5xX + -5x2 + 5x2X

Combine like terms: -5x + 5x = 0
fX = 0 + 5xX + -5x2 + 5x2X
fX = 5xX + -5x2 + 5x2X

Solving
fX = 5xX + -5x2 + 5x2X

Solving for variable 'f'.

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

Divide each side by 'X'.
f = 5x + -5x2X-1 + 5x2

Simplifying
f = 5x + -5x2X-1 + 5x2

Reorder the terms:
f = 5x + 5x2 + -5x2X-1

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