9x^2+42x+15=0

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Solution for 9x^2+42x+15=0 equation: 


Simplifying
9x2 + 42x + 15 = 0

Reorder the terms:
15 + 42x + 9x2 = 0

Solving
15 + 42x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 14x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + 14x + 3x2)' equal to zero and attempt to solve:

Simplifying
5 + 14x + 3x2 = 0

Solving
5 + 14x + 3x2 = 0

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

Divide each side by '3'.
1.666666667 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 4.666666667x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 4.666666667x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 4.666666667x + x2 = 0 + -1.666666667
4.666666667x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
4.666666667x + x2 = -1.666666667

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = -1.666666667 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = -1.666666667 + 5.444444448

Combine like terms: -1.666666667 + 5.444444448 = 3.777777781
5.444444448 + 4.666666667x + x2 = 3.777777781

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 3.777777781

Calculate the square root of the right side: 1.943650632

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 1.943650632 and -1.943650632.


Subproblem 1
x + 2.333333334 = 1.943650632

Simplifying
x + 2.333333334 = 1.943650632

Reorder the terms:
2.333333334 + x = 1.943650632

Solving
2.333333334 + x = 1.943650632

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 1.943650632 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 1.943650632 + -2.333333334
x = 1.943650632 + -2.333333334

Combine like terms: 1.943650632 + -2.333333334 = -0.389682702
x = -0.389682702

Simplifying
x = -0.389682702


Subproblem 2
x + 2.333333334 = -1.943650632

Simplifying
x + 2.333333334 = -1.943650632

Reorder the terms:
2.333333334 + x = -1.943650632

Solving
2.333333334 + x = -1.943650632

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -1.943650632 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -1.943650632 + -2.333333334
x = -1.943650632 + -2.333333334

Combine like terms: -1.943650632 + -2.333333334 = -4.276983966
x = -4.276983966

Simplifying
x = -4.276983966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.389682702, -4.276983966}
Solution
x = {-0.389682702, -4.276983966}

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