X-3(X-3+16)=(X+3)(X+3)

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Solution for X-3(X-3+16)=(X+3)(X+3) equation: 


Simplifying
X + -3(X + -3 + 16) = (X + 3)(X + 3)

Reorder the terms:
X + -3(-3 + 16 + X) = (X + 3)(X + 3)

Combine like terms: -3 + 16 = 13
X + -3(13 + X) = (X + 3)(X + 3)
X + (13 * -3 + X * -3) = (X + 3)(X + 3)
X + (-39 + -3X) = (X + 3)(X + 3)

Reorder the terms:
-39 + X + -3X = (X + 3)(X + 3)

Combine like terms: X + -3X = -2X
-39 + -2X = (X + 3)(X + 3)

Reorder the terms:
-39 + -2X = (3 + X)(X + 3)

Reorder the terms:
-39 + -2X = (3 + X)(3 + X)

Multiply (3 + X) * (3 + X)
-39 + -2X = (3(3 + X) + X(3 + X))
-39 + -2X = ((3 * 3 + X * 3) + X(3 + X))
-39 + -2X = ((9 + 3X) + X(3 + X))
-39 + -2X = (9 + 3X + (3 * X + X * X))
-39 + -2X = (9 + 3X + (3X + X2))

Combine like terms: 3X + 3X = 6X
-39 + -2X = (9 + 6X + X2)

Solving
-39 + -2X = 9 + 6X + X2

Solving for variable 'X'.

Reorder the terms:
-39 + -9 + -2X + -6X + -1X2 = 9 + 6X + X2 + -9 + -6X + -1X2

Combine like terms: -39 + -9 = -48
-48 + -2X + -6X + -1X2 = 9 + 6X + X2 + -9 + -6X + -1X2

Combine like terms: -2X + -6X = -8X
-48 + -8X + -1X2 = 9 + 6X + X2 + -9 + -6X + -1X2

Reorder the terms:
-48 + -8X + -1X2 = 9 + -9 + 6X + -6X + X2 + -1X2

Combine like terms: 9 + -9 = 0
-48 + -8X + -1X2 = 0 + 6X + -6X + X2 + -1X2
-48 + -8X + -1X2 = 6X + -6X + X2 + -1X2

Combine like terms: 6X + -6X = 0
-48 + -8X + -1X2 = 0 + X2 + -1X2
-48 + -8X + -1X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-48 + -8X + -1X2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(48 + 8X + X2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(48 + 8X + X2)' equal to zero and attempt to solve:

Simplifying
48 + 8X + X2 = 0

Solving
48 + 8X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-48' to each side of the equation.
48 + 8X + -48 + X2 = 0 + -48

Reorder the terms:
48 + -48 + 8X + X2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + 8X + X2 = 0 + -48
8X + X2 = 0 + -48

Combine like terms: 0 + -48 = -48
8X + X2 = -48

The X term is 8X.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8X + 16 + X2 = -48 + 16

Reorder the terms:
16 + 8X + X2 = -48 + 16

Combine like terms: -48 + 16 = -32
16 + 8X + X2 = -32

Factor a perfect square on the left side:
(X + 4)(X + 4) = -32

Can't calculate square root of the right side.

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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