p(x)=3(x+5)(x+7)

Solution for p(x)=3(x+5)(x+7) equation:

Simplifying
p(x) = 3(x + 5)(x + 7)

Multiply p * x
px = 3(x + 5)(x + 7)

Reorder the terms:
px = 3(5 + x)(x + 7)

Reorder the terms:
px = 3(5 + x)(7 + x)

Multiply (5 + x) * (7 + x)
px = 3(5(7 + x) + x(7 + x))
px = 3((7 * 5 + x * 5) + x(7 + x))
px = 3((35 + 5x) + x(7 + x))
px = 3(35 + 5x + (7 * x + x * x))
px = 3(35 + 5x + (7x + x2))

Combine like terms: 5x + 7x = 12x
px = 3(35 + 12x + x2)
px = (35 * 3 + 12x * 3 + x2 * 3)
px = (105 + 36x + 3x2)

Solving
px = 105 + 36x + 3x2

Solving for variable 'p'.

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

Divide each side by 'x'.
p = 105x-1 + 36 + 3x

Simplifying
p = 105x-1 + 36 + 3x

Reorder the terms:
p = 36 + 105x-1 + 3x