(x-5)(x+p)=x^2-qx-10

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


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

Reorder the terms:
(-5 + x)(x + p) = x2 + -1qx + -10

Reorder the terms:
(-5 + x)(p + x) = x2 + -1qx + -10

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

Reorder the terms:
(-5p + px + -5x + x2) = x2 + -1qx + -10
(-5p + px + -5x + x2) = x2 + -1qx + -10

Reorder the terms:
-5p + px + -5x + x2 = -10 + -1qx + x2

Add '-1x2' to each side of the equation.
-5p + px + -5x + x2 + -1x2 = -10 + -1qx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5p + px + -5x + 0 = -10 + -1qx + x2 + -1x2
-5p + px + -5x = -10 + -1qx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5p + px + -5x = -10 + -1qx + 0
-5p + px + -5x = -10 + -1qx

Solving
-5p + px + -5x = -10 + -1qx

Solving for variable 'p'.

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

Add '5x' to each side of the equation.
-5p + px + -5x + 5x = -10 + -1qx + 5x

Combine like terms: -5x + 5x = 0
-5p + px + 0 = -10 + -1qx + 5x
-5p + px = -10 + -1qx + 5x

Reorder the terms:
10 + -5p + px + qx + -5x = -10 + -1qx + 5x + 10 + qx + -5x

Reorder the terms:
10 + -5p + px + qx + -5x = -10 + 10 + -1qx + qx + 5x + -5x

Combine like terms: -10 + 10 = 0
10 + -5p + px + qx + -5x = 0 + -1qx + qx + 5x + -5x
10 + -5p + px + qx + -5x = -1qx + qx + 5x + -5x

Combine like terms: -1qx + qx = 0
10 + -5p + px + qx + -5x = 0 + 5x + -5x
10 + -5p + px + qx + -5x = 5x + -5x

Combine like terms: 5x + -5x = 0
10 + -5p + px + qx + -5x = 0

The solution to this equation could not be determined.

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