f(x)=(2x+2)(3x-4)-(x-3)(x-6)

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Solution for f(x)=(2x+2)(3x-4)-(x-3)(x-6) equation: 


Simplifying
f(x) = (2x + 2)(3x + -4) + -1(x + -3)(x + -6)

Multiply f * x
fx = (2x + 2)(3x + -4) + -1(x + -3)(x + -6)

Reorder the terms:
fx = (2 + 2x)(3x + -4) + -1(x + -3)(x + -6)

Reorder the terms:
fx = (2 + 2x)(-4 + 3x) + -1(x + -3)(x + -6)

Multiply (2 + 2x) * (-4 + 3x)
fx = (2(-4 + 3x) + 2x * (-4 + 3x)) + -1(x + -3)(x + -6)
fx = ((-4 * 2 + 3x * 2) + 2x * (-4 + 3x)) + -1(x + -3)(x + -6)
fx = ((-8 + 6x) + 2x * (-4 + 3x)) + -1(x + -3)(x + -6)
fx = (-8 + 6x + (-4 * 2x + 3x * 2x)) + -1(x + -3)(x + -6)
fx = (-8 + 6x + (-8x + 6x2)) + -1(x + -3)(x + -6)

Combine like terms: 6x + -8x = -2x
fx = (-8 + -2x + 6x2) + -1(x + -3)(x + -6)

Reorder the terms:
fx = -8 + -2x + 6x2 + -1(-3 + x)(x + -6)

Reorder the terms:
fx = -8 + -2x + 6x2 + -1(-3 + x)(-6 + x)

Multiply (-3 + x) * (-6 + x)
fx = -8 + -2x + 6x2 + -1(-3(-6 + x) + x(-6 + x))
fx = -8 + -2x + 6x2 + -1((-6 * -3 + x * -3) + x(-6 + x))
fx = -8 + -2x + 6x2 + -1((18 + -3x) + x(-6 + x))
fx = -8 + -2x + 6x2 + -1(18 + -3x + (-6 * x + x * x))
fx = -8 + -2x + 6x2 + -1(18 + -3x + (-6x + x2))

Combine like terms: -3x + -6x = -9x
fx = -8 + -2x + 6x2 + -1(18 + -9x + x2)
fx = -8 + -2x + 6x2 + (18 * -1 + -9x * -1 + x2 * -1)
fx = -8 + -2x + 6x2 + (-18 + 9x + -1x2)

Reorder the terms:
fx = -8 + -18 + -2x + 9x + 6x2 + -1x2

Combine like terms: -8 + -18 = -26
fx = -26 + -2x + 9x + 6x2 + -1x2

Combine like terms: -2x + 9x = 7x
fx = -26 + 7x + 6x2 + -1x2

Combine like terms: 6x2 + -1x2 = 5x2
fx = -26 + 7x + 5x2

Solving
fx = -26 + 7x + 5x2

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -26x-1 + 7 + 5x

Simplifying
f = -26x-1 + 7 + 5x

Reorder the terms:
f = 7 + -26x-1 + 5x

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