x^3-12x-16=(x+2)(x^2+qx+r)

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Solution for x^3-12x-16=(x+2)(x^2+qx+r) equation: 


Simplifying
x3 + -12x + -16 = (x + 2)(x2 + qx + r)

Reorder the terms:
-16 + -12x + x3 = (x + 2)(x2 + qx + r)

Reorder the terms:
-16 + -12x + x3 = (2 + x)(x2 + qx + r)

Reorder the terms:
-16 + -12x + x3 = (2 + x)(qx + r + x2)

Multiply (2 + x) * (qx + r + x2)
-16 + -12x + x3 = (2(qx + r + x2) + x(qx + r + x2))
-16 + -12x + x3 = ((qx * 2 + r * 2 + x2 * 2) + x(qx + r + x2))
-16 + -12x + x3 = ((2qx + 2r + 2x2) + x(qx + r + x2))
-16 + -12x + x3 = (2qx + 2r + 2x2 + (qx * x + r * x + x2 * x))
-16 + -12x + x3 = (2qx + 2r + 2x2 + (qx2 + rx + x3))

Reorder the terms:
-16 + -12x + x3 = (2qx + qx2 + 2r + rx + 2x2 + x3)
-16 + -12x + x3 = (2qx + qx2 + 2r + rx + 2x2 + x3)

Add '-1x3' to each side of the equation.
-16 + -12x + x3 + -1x3 = 2qx + qx2 + 2r + rx + 2x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-16 + -12x + 0 = 2qx + qx2 + 2r + rx + 2x2 + x3 + -1x3
-16 + -12x = 2qx + qx2 + 2r + rx + 2x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-16 + -12x = 2qx + qx2 + 2r + rx + 2x2 + 0
-16 + -12x = 2qx + qx2 + 2r + rx + 2x2

Solving
-16 + -12x = 2qx + qx2 + 2r + rx + 2x2

Solving for variable 'x'.

Reorder the terms:
-16 + -2qx + -1qx2 + -2r + -1rx + -12x + -2x2 = 2qx + qx2 + 2r + rx + 2x2 + -2qx + -1qx2 + -2r + -1rx + -2x2

Reorder the terms:
-16 + -2qx + -1qx2 + -2r + -1rx + -12x + -2x2 = 2qx + -2qx + qx2 + -1qx2 + 2r + -2r + rx + -1rx + 2x2 + -2x2

Combine like terms: 2qx + -2qx = 0
-16 + -2qx + -1qx2 + -2r + -1rx + -12x + -2x2 = 0 + qx2 + -1qx2 + 2r + -2r + rx + -1rx + 2x2 + -2x2
-16 + -2qx + -1qx2 + -2r + -1rx + -12x + -2x2 = qx2 + -1qx2 + 2r + -2r + rx + -1rx + 2x2 + -2x2

Combine like terms: qx2 + -1qx2 = 0
-16 + -2qx + -1qx2 + -2r + -1rx + -12x + -2x2 = 0 + 2r + -2r + rx + -1rx + 2x2 + -2x2
-16 + -2qx + -1qx2 + -2r + -1rx + -12x + -2x2 = 2r + -2r + rx + -1rx + 2x2 + -2x2

Combine like terms: 2r + -2r = 0
-16 + -2qx + -1qx2 + -2r + -1rx + -12x + -2x2 = 0 + rx + -1rx + 2x2 + -2x2
-16 + -2qx + -1qx2 + -2r + -1rx + -12x + -2x2 = rx + -1rx + 2x2 + -2x2

Combine like terms: rx + -1rx = 0
-16 + -2qx + -1qx2 + -2r + -1rx + -12x + -2x2 = 0 + 2x2 + -2x2
-16 + -2qx + -1qx2 + -2r + -1rx + -12x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-16 + -2qx + -1qx2 + -2r + -1rx + -12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(16 + 2qx + qx2 + 2r + rx + 12x + 2x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(16 + 2qx + qx2 + 2r + rx + 12x + 2x2)' equal to zero and attempt to solve:

Simplifying
16 + 2qx + qx2 + 2r + rx + 12x + 2x2 = 0

Solving
16 + 2qx + qx2 + 2r + rx + 12x + 2x2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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