(x-2c)(2x+c)+cx=

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Solution for (x-2c)(2x+c)+cx= equation: 


Simplifying
(x + -2c)(2x + c) + cx = 0

Reorder the terms:
(-2c + x)(2x + c) + cx = 0

Reorder the terms:
(-2c + x)(c + 2x) + cx = 0

Multiply (-2c + x) * (c + 2x)
(-2c * (c + 2x) + x(c + 2x)) + cx = 0
((c * -2c + 2x * -2c) + x(c + 2x)) + cx = 0

Reorder the terms:
((-4cx + -2c2) + x(c + 2x)) + cx = 0
((-4cx + -2c2) + x(c + 2x)) + cx = 0
(-4cx + -2c2 + (c * x + 2x * x)) + cx = 0
(-4cx + -2c2 + (cx + 2x2)) + cx = 0

Reorder the terms:
(-4cx + cx + -2c2 + 2x2) + cx = 0

Combine like terms: -4cx + cx = -3cx
(-3cx + -2c2 + 2x2) + cx = 0

Reorder the terms:
-3cx + cx + -2c2 + 2x2 = 0

Combine like terms: -3cx + cx = -2cx
-2cx + -2c2 + 2x2 = 0

Solving
-2cx + -2c2 + 2x2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1cx + -1c2 + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1cx + -1c2 + x2)' equal to zero and attempt to solve:

Simplifying
-1cx + -1c2 + x2 = 0

Solving
-1cx + -1c2 + x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
cx + c2 + -1x2 = 0

Move the constant term to the right:

Add '-1x2' to each side of the equation.
cx + c2 + -1x2 + -1x2 = 0 + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
cx + c2 + -2x2 = 0 + -1x2
Remove the zero:
cx + c2 + -2x2 = -1x2

The c term is cx.  Take half its coefficient (0.5x).
Square it (0.25x2) and add it to both sides.

Add '0.25x2' to each side of the equation.
x2 + c2 + -2x2 + 0.25x2 = -1x2 + 0.25x2

Reorder the terms:
c2 + x2 + -2x2 + 0.25x2 = -1x2 + 0.25x2

Combine like terms: x2 + -2x2 = -1x2
c2 + -1x2 + 0.25x2 = -1x2 + 0.25x2

Combine like terms: -1x2 + 0.25x2 = -0.75x2
c2 + -0.75x2 = -1x2 + 0.25x2

Combine like terms: -1x2 + 0.25x2 = -0.75x2
c2 + -0.75x2 = -0.75x2

Factor a perfect square on the left side:
(c + 0.5x)(c + 0.5x) = -0.75x2

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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