f(x)=x(2x+3)(4x+5)+(6x+7)(8x+9)

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Solution for f(x)=x(2x+3)(4x+5)+(6x+7)(8x+9) equation: 


Simplifying
f(x) = x(2x + 3)(4x + 5) + (6x + 7)(8x + 9)

Multiply f * x
fx = x(2x + 3)(4x + 5) + (6x + 7)(8x + 9)

Reorder the terms:
fx = x(3 + 2x)(4x + 5) + (6x + 7)(8x + 9)

Reorder the terms:
fx = x(3 + 2x)(5 + 4x) + (6x + 7)(8x + 9)

Multiply (3 + 2x) * (5 + 4x)
fx = x(3(5 + 4x) + 2x * (5 + 4x)) + (6x + 7)(8x + 9)
fx = x((5 * 3 + 4x * 3) + 2x * (5 + 4x)) + (6x + 7)(8x + 9)
fx = x((15 + 12x) + 2x * (5 + 4x)) + (6x + 7)(8x + 9)
fx = x(15 + 12x + (5 * 2x + 4x * 2x)) + (6x + 7)(8x + 9)
fx = x(15 + 12x + (10x + 8x2)) + (6x + 7)(8x + 9)

Combine like terms: 12x + 10x = 22x
fx = x(15 + 22x + 8x2) + (6x + 7)(8x + 9)
fx = (15 * x + 22x * x + 8x2 * x) + (6x + 7)(8x + 9)
fx = (15x + 22x2 + 8x3) + (6x + 7)(8x + 9)

Reorder the terms:
fx = 15x + 22x2 + 8x3 + (7 + 6x)(8x + 9)

Reorder the terms:
fx = 15x + 22x2 + 8x3 + (7 + 6x)(9 + 8x)

Multiply (7 + 6x) * (9 + 8x)
fx = 15x + 22x2 + 8x3 + (7(9 + 8x) + 6x * (9 + 8x))
fx = 15x + 22x2 + 8x3 + ((9 * 7 + 8x * 7) + 6x * (9 + 8x))
fx = 15x + 22x2 + 8x3 + ((63 + 56x) + 6x * (9 + 8x))
fx = 15x + 22x2 + 8x3 + (63 + 56x + (9 * 6x + 8x * 6x))
fx = 15x + 22x2 + 8x3 + (63 + 56x + (54x + 48x2))

Combine like terms: 56x + 54x = 110x
fx = 15x + 22x2 + 8x3 + (63 + 110x + 48x2)

Reorder the terms:
fx = 63 + 15x + 110x + 22x2 + 48x2 + 8x3

Combine like terms: 15x + 110x = 125x
fx = 63 + 125x + 22x2 + 48x2 + 8x3

Combine like terms: 22x2 + 48x2 = 70x2
fx = 63 + 125x + 70x2 + 8x3

Solving
fx = 63 + 125x + 70x2 + 8x3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 63x-1 + 125 + 70x + 8x2

Simplifying
f = 63x-1 + 125 + 70x + 8x2

Reorder the terms:
f = 125 + 63x-1 + 70x + 8x2

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