p(x)=3(x^2+10x+5)-5(x-k)

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Solution for p(x)=3(x^2+10x+5)-5(x-k) equation: 


Simplifying
p(x) = 3(x2 + 10x + 5) + -5(x + -1k)

Multiply p * x
px = 3(x2 + 10x + 5) + -5(x + -1k)

Reorder the terms:
px = 3(5 + 10x + x2) + -5(x + -1k)
px = (5 * 3 + 10x * 3 + x2 * 3) + -5(x + -1k)
px = (15 + 30x + 3x2) + -5(x + -1k)

Reorder the terms:
px = 15 + 30x + 3x2 + -5(-1k + x)
px = 15 + 30x + 3x2 + (-1k * -5 + x * -5)
px = 15 + 30x + 3x2 + (5k + -5x)

Reorder the terms:
px = 15 + 5k + 30x + -5x + 3x2

Combine like terms: 30x + -5x = 25x
px = 15 + 5k + 25x + 3x2

Solving
px = 15 + 5k + 25x + 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 = 15x-1 + 5kx-1 + 25 + 3x

Simplifying
p = 15x-1 + 5kx-1 + 25 + 3x

Reorder the terms:
p = 25 + 5kx-1 + 15x-1 + 3x

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