x(5x^2+6x+45)=0

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Solution for x(5x^2+6x+45)=0 equation: 


Simplifying
x(5x2 + 6x + 45) = 0

Reorder the terms:
x(45 + 6x + 5x2) = 0
(45 * x + 6x * x + 5x2 * x) = 0
(45x + 6x2 + 5x3) = 0

Solving
45x + 6x2 + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(45 + 6x + 5x2) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(45 + 6x + 5x2)' equal to zero and attempt to solve:

Simplifying
45 + 6x + 5x2 = 0

Solving
45 + 6x + 5x2 = 0

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

Divide each side by '5'.
9 + 1.2x + x2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 1.2x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 1.2x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 1.2x + x2 = 0 + -9
1.2x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
1.2x + x2 = -9

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 = -9 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = -9 + 0.36

Combine like terms: -9 + 0.36 = -8.64
0.36 + 1.2x + x2 = -8.64

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = -8.64

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.
Solution
x = {0}

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