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

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


Simplifying
x(2x + -3) + 4(x2 + 1) = 0

Reorder the terms:
x(-3 + 2x) + 4(x2 + 1) = 0
(-3 * x + 2x * x) + 4(x2 + 1) = 0
(-3x + 2x2) + 4(x2 + 1) = 0

Reorder the terms:
-3x + 2x2 + 4(1 + x2) = 0
-3x + 2x2 + (1 * 4 + x2 * 4) = 0
-3x + 2x2 + (4 + 4x2) = 0

Reorder the terms:
4 + -3x + 2x2 + 4x2 = 0

Combine like terms: 2x2 + 4x2 = 6x2
4 + -3x + 6x2 = 0

Solving
4 + -3x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
0.6666666667 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -0.5x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -0.5x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -0.5x + x2 = 0 + -0.6666666667
-0.5x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-0.5x + x2 = -0.6666666667

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -0.6666666667 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -0.6666666667 + 0.0625

Combine like terms: -0.6666666667 + 0.0625 = -0.6041666667
0.0625 + -0.5x + x2 = -0.6041666667

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -0.6041666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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