0=5x^2+6x+3

Solution for 0=5x^2+6x+3 equation:

Simplifying
0 = 5x2 + 6x + 3

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

Solving
0 = 3 + 6x + 5x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Simplifying
3 + 6x + 5x2 = 0

Solving
3 + 6x + 5x2 = 0

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

Divide each side by '5'.
0.6 + 1.2x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 1.2x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 1.2x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 1.2x + x2 = 0 + -0.6
1.2x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
1.2x + x2 = -0.6

The x term is 1.2x.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2x + 0.36 + x2 = -0.6 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = -0.6 + 0.36

Combine like terms: -0.6 + 0.36 = -0.24
0.36 + 1.2x + x2 = -0.24

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = -0.24

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.