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

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


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

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

Reorder the terms:
0 = 5 + 6x + 3x2

Solving
0 = 5 + 6x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -6x + -3x2 = 5 + 6x + 3x2 + -5 + -6x + -3x2

Reorder the terms:
-5 + -6x + -3x2 = 5 + -5 + 6x + -6x + 3x2 + -3x2

Combine like terms: 5 + -5 = 0
-5 + -6x + -3x2 = 0 + 6x + -6x + 3x2 + -3x2
-5 + -6x + -3x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
-5 + -6x + -3x2 = 0 + 3x2 + -3x2
-5 + -6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-5 + -6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 6x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 6x + 3x2)' equal to zero and attempt to solve:

Simplifying
5 + 6x + 3x2 = 0

Solving
5 + 6x + 3x2 = 0

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

Divide each side by '3'.
1.666666667 + 2x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 2x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 2x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 2x + x2 = 0 + -1.666666667
2x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
2x + x2 = -1.666666667

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -1.666666667 + 1

Reorder the terms:
1 + 2x + x2 = -1.666666667 + 1

Combine like terms: -1.666666667 + 1 = -0.666666667
1 + 2x + x2 = -0.666666667

Factor a perfect square on the left side:
(x + 1)(x + 1) = -0.666666667

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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