4x(x+1)=2*(x-3)

Solution for 4x(x+1)=2*(x-3) equation:

Simplifying
4x(x + 1) = 2(x + -3)

Reorder the terms:
4x(1 + x) = 2(x + -3)
(1 * 4x + x * 4x) = 2(x + -3)
(4x + 4x2) = 2(x + -3)

Reorder the terms:
4x + 4x2 = 2(-3 + x)
4x + 4x2 = (-3 * 2 + x * 2)
4x + 4x2 = (-6 + 2x)

Solving
4x + 4x2 = -6 + 2x

Solving for variable 'x'.

Reorder the terms:
6 + 4x + -2x + 4x2 = -6 + 2x + 6 + -2x

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

Reorder the terms:
6 + 2x + 4x2 = -6 + 6 + 2x + -2x

Combine like terms: -6 + 6 = 0
6 + 2x + 4x2 = 0 + 2x + -2x
6 + 2x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
6 + 2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + x + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + x + 2x2 = 0

Solving
3 + x + 2x2 = 0

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

Divide each side by '2'.
1.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.5x + x2 = 0 + -1.5
0.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.5x + x2 = -1.5

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.
0.5x + 0.25 + x2 = -1.5 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + 0.5x + x2 = -1.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -1.25

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.