X^2+4x(x+1)=0

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Solution for X^2+4x(x+1)=0 equation: 


Simplifying
X2 + 4x(x + 1) = 0

Reorder the terms:
X2 + 4x(1 + x) = 0
X2 + (1 * 4x + x * 4x) = 0
X2 + (4x + 4x2) = 0

Solving
X2 + 4x + 4x2 = 0

Solving for variable 'X'.

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

Add '-4x' to each side of the equation.
X2 + 4x + -4x + 4x2 = 0 + -4x

Combine like terms: 4x + -4x = 0
X2 + 0 + 4x2 = 0 + -4x
X2 + 4x2 = 0 + -4x
Remove the zero:
X2 + 4x2 = -4x

Add '-4x2' to each side of the equation.
X2 + 4x2 + -4x2 = -4x + -4x2

Combine like terms: 4x2 + -4x2 = 0
X2 + 0 = -4x + -4x2
X2 = -4x + -4x2

Simplifying
X2 = -4x + -4x2

Reorder the terms:
X2 + 4x + 4x2 = -4x + 4x + -4x2 + 4x2

Combine like terms: -4x + 4x = 0
X2 + 4x + 4x2 = 0 + -4x2 + 4x2
X2 + 4x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
X2 + 4x + 4x2 = 0

Factor a trinomial.
(X + 2x)(X + 2x) = 0


Subproblem 1
Set the factor '(X + 2x)' equal to zero and attempt to solve:

Simplifying
X + 2x = 0

Solving
X + 2x = 0

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

Add '-2x' to each side of the equation.
X + 2x + -2x = 0 + -2x

Combine like terms: 2x + -2x = 0
X + 0 = 0 + -2x
X = 0 + -2x
Remove the zero:
X = -2x

Simplifying
X = -2x

Subproblem 2
Set the factor '(X + 2x)' equal to zero and attempt to solve:

Simplifying
X + 2x = 0

Solving
X + 2x = 0

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

Add '-2x' to each side of the equation.
X + 2x + -2x = 0 + -2x

Combine like terms: 2x + -2x = 0
X + 0 = 0 + -2x
X = 0 + -2x
Remove the zero:
X = -2x

Simplifying
X = -2x
Solution
X = {-2x, -2x}

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