2(3x^2+5x+4)=0

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Solution for 2(3x^2+5x+4)=0 equation: 


Simplifying
2(3x2 + 5x + 4) = 0

Reorder the terms:
2(4 + 5x + 3x2) = 0
(4 * 2 + 5x * 2 + 3x2 * 2) = 0
(8 + 10x + 6x2) = 0

Solving
8 + 10x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 5x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + 5x + 3x2)' equal to zero and attempt to solve:

Simplifying
4 + 5x + 3x2 = 0

Solving
4 + 5x + 3x2 = 0

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

Divide each side by '3'.
1.333333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 1.666666667x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 1.666666667x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + -1.333333333
1.666666667x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
1.666666667x + x2 = -1.333333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = -1.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = -1.333333333 + 0.6944444447

Combine like terms: -1.333333333 + 0.6944444447 = -0.6388888883
0.6944444447 + 1.666666667x + x2 = -0.6388888883

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = -0.6388888883

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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