(X-p)*(2x^2+9x+10)=(x^2-4)*(2x+q)

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Solution for (X-p)*(2x^2+9x+10)=(x^2-4)*(2x+q) equation: 


Simplifying
(X + -1p)(2x2 + 9x + 10) = (x2 + -4)(2x + q)

Reorder the terms:
(X + -1p)(10 + 9x + 2x2) = (x2 + -4)(2x + q)

Multiply (X + -1p) * (10 + 9x + 2x2)
(X(10 + 9x + 2x2) + -1p * (10 + 9x + 2x2)) = (x2 + -4)(2x + q)
((10 * X + 9x * X + 2x2 * X) + -1p * (10 + 9x + 2x2)) = (x2 + -4)(2x + q)
((10X + 9xX + 2x2X) + -1p * (10 + 9x + 2x2)) = (x2 + -4)(2x + q)
(10X + 9xX + 2x2X + (10 * -1p + 9x * -1p + 2x2 * -1p)) = (x2 + -4)(2x + q)
(10X + 9xX + 2x2X + (-10p + -9px + -2px2)) = (x2 + -4)(2x + q)

Reorder the terms:
(10X + -10p + -9px + -2px2 + 9xX + 2x2X) = (x2 + -4)(2x + q)
(10X + -10p + -9px + -2px2 + 9xX + 2x2X) = (x2 + -4)(2x + q)

Reorder the terms:
10X + -10p + -9px + -2px2 + 9xX + 2x2X = (-4 + x2)(2x + q)

Reorder the terms:
10X + -10p + -9px + -2px2 + 9xX + 2x2X = (-4 + x2)(q + 2x)

Multiply (-4 + x2) * (q + 2x)
10X + -10p + -9px + -2px2 + 9xX + 2x2X = (-4(q + 2x) + x2(q + 2x))
10X + -10p + -9px + -2px2 + 9xX + 2x2X = ((q * -4 + 2x * -4) + x2(q + 2x))
10X + -10p + -9px + -2px2 + 9xX + 2x2X = ((-4q + -8x) + x2(q + 2x))
10X + -10p + -9px + -2px2 + 9xX + 2x2X = (-4q + -8x + (q * x2 + 2x * x2))
10X + -10p + -9px + -2px2 + 9xX + 2x2X = (-4q + -8x + (qx2 + 2x3))

Reorder the terms:
10X + -10p + -9px + -2px2 + 9xX + 2x2X = (-4q + qx2 + -8x + 2x3)
10X + -10p + -9px + -2px2 + 9xX + 2x2X = (-4q + qx2 + -8x + 2x3)

Solving
10X + -10p + -9px + -2px2 + 9xX + 2x2X = -4q + qx2 + -8x + 2x3

Solving for variable 'X'.

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

Add '10p' to each side of the equation.
10X + -10p + -9px + -2px2 + 9xX + 10p + 2x2X = -4q + qx2 + -8x + 10p + 2x3

Reorder the terms:
10X + -10p + 10p + -9px + -2px2 + 9xX + 2x2X = -4q + qx2 + -8x + 10p + 2x3

Combine like terms: -10p + 10p = 0
10X + 0 + -9px + -2px2 + 9xX + 2x2X = -4q + qx2 + -8x + 10p + 2x3
10X + -9px + -2px2 + 9xX + 2x2X = -4q + qx2 + -8x + 10p + 2x3

Reorder the terms:
10X + -9px + -2px2 + 9xX + 2x2X = 10p + -4q + qx2 + -8x + 2x3

Add '9px' to each side of the equation.
10X + -9px + -2px2 + 9xX + 9px + 2x2X = 10p + -4q + qx2 + -8x + 9px + 2x3

Reorder the terms:
10X + -9px + 9px + -2px2 + 9xX + 2x2X = 10p + -4q + qx2 + -8x + 9px + 2x3

Combine like terms: -9px + 9px = 0
10X + 0 + -2px2 + 9xX + 2x2X = 10p + -4q + qx2 + -8x + 9px + 2x3
10X + -2px2 + 9xX + 2x2X = 10p + -4q + qx2 + -8x + 9px + 2x3

Reorder the terms:
10X + -2px2 + 9xX + 2x2X = 10p + 9px + -4q + qx2 + -8x + 2x3

Add '2px2' to each side of the equation.
10X + -2px2 + 9xX + 2px2 + 2x2X = 10p + 9px + -4q + qx2 + -8x + 2px2 + 2x3

Reorder the terms:
10X + -2px2 + 2px2 + 9xX + 2x2X = 10p + 9px + -4q + qx2 + -8x + 2px2 + 2x3

Combine like terms: -2px2 + 2px2 = 0
10X + 0 + 9xX + 2x2X = 10p + 9px + -4q + qx2 + -8x + 2px2 + 2x3
10X + 9xX + 2x2X = 10p + 9px + -4q + qx2 + -8x + 2px2 + 2x3

Reorder the terms:
10X + 9xX + 2x2X = 10p + 9px + 2px2 + -4q + qx2 + -8x + 2x3

Reorder the terms:
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = 10p + 9px + 2px2 + -4q + qx2 + -8x + 2x3 + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + -2x3

Reorder the terms:
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = 10p + -10p + 9px + -9px + 2px2 + -2px2 + -4q + 4q + qx2 + -1qx2 + -8x + 8x + 2x3 + -2x3

Combine like terms: 10p + -10p = 0
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = 0 + 9px + -9px + 2px2 + -2px2 + -4q + 4q + qx2 + -1qx2 + -8x + 8x + 2x3 + -2x3
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = 9px + -9px + 2px2 + -2px2 + -4q + 4q + qx2 + -1qx2 + -8x + 8x + 2x3 + -2x3

Combine like terms: 9px + -9px = 0
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = 0 + 2px2 + -2px2 + -4q + 4q + qx2 + -1qx2 + -8x + 8x + 2x3 + -2x3
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = 2px2 + -2px2 + -4q + 4q + qx2 + -1qx2 + -8x + 8x + 2x3 + -2x3

Combine like terms: 2px2 + -2px2 = 0
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = 0 + -4q + 4q + qx2 + -1qx2 + -8x + 8x + 2x3 + -2x3
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = -4q + 4q + qx2 + -1qx2 + -8x + 8x + 2x3 + -2x3

Combine like terms: -4q + 4q = 0
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = 0 + qx2 + -1qx2 + -8x + 8x + 2x3 + -2x3
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = qx2 + -1qx2 + -8x + 8x + 2x3 + -2x3

Combine like terms: qx2 + -1qx2 = 0
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = 0 + -8x + 8x + 2x3 + -2x3
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = -8x + 8x + 2x3 + -2x3

Combine like terms: -8x + 8x = 0
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = 0 + 2x3 + -2x3
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
10X + -10p + -9px + -2px2 + 4q + -1qx2 + 8x + 9xX + 2x2X + -2x3 = 0

The solution to this equation could not be determined.

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