2x(x+4)=2(x-4)+4x

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Solution for 2x(x+4)=2(x-4)+4x equation: 


Simplifying
2x(x + 4) = 2(x + -4) + 4x

Reorder the terms:
2x(4 + x) = 2(x + -4) + 4x
(4 * 2x + x * 2x) = 2(x + -4) + 4x
(8x + 2x2) = 2(x + -4) + 4x

Reorder the terms:
8x + 2x2 = 2(-4 + x) + 4x
8x + 2x2 = (-4 * 2 + x * 2) + 4x
8x + 2x2 = (-8 + 2x) + 4x

Combine like terms: 2x + 4x = 6x
8x + 2x2 = -8 + 6x

Solving
8x + 2x2 = -8 + 6x

Solving for variable 'x'.

Reorder the terms:
8 + 8x + -6x + 2x2 = -8 + 6x + 8 + -6x

Combine like terms: 8x + -6x = 2x
8 + 2x + 2x2 = -8 + 6x + 8 + -6x

Reorder the terms:
8 + 2x + 2x2 = -8 + 8 + 6x + -6x

Combine like terms: -8 + 8 = 0
8 + 2x + 2x2 = 0 + 6x + -6x
8 + 2x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
8 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + x + x2)' equal to zero and attempt to solve:

Simplifying
4 + x + x2 = 0

Solving
4 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x + x2 = 0 + -4
x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
x + x2 = -4

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = -4 + 0.25

Reorder the terms:
0.25 + x + x2 = -4 + 0.25

Combine like terms: -4 + 0.25 = -3.75
0.25 + x + x2 = -3.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -3.75

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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