(5x^2+9)3=-6x

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Solution for (5x^2+9)3=-6x equation: 


Simplifying
(5x2 + 9) * 3 = -6x

Reorder the terms:
(9 + 5x2) * 3 = -6x

Reorder the terms for easier multiplication:
3(9 + 5x2) = -6x
(9 * 3 + 5x2 * 3) = -6x
(27 + 15x2) = -6x

Solving
27 + 15x2 = -6x

Solving for variable 'x'.

Reorder the terms:
27 + 6x + 15x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
27 + 6x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 2x + 5x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(9 + 2x + 5x2)' equal to zero and attempt to solve:

Simplifying
9 + 2x + 5x2 = 0

Solving
9 + 2x + 5x2 = 0

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

Divide each side by '5'.
1.8 + 0.4x + x2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + 0.4x + -1.8 + x2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + 0.4x + x2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + 0.4x + x2 = 0 + -1.8
0.4x + x2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
0.4x + x2 = -1.8

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = -1.8 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = -1.8 + 0.04

Combine like terms: -1.8 + 0.04 = -1.76
0.04 + 0.4x + x2 = -1.76

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = -1.76

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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