(x+9.6)(3x+0.9)=

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Solution for (x+9.6)(3x+0.9)= equation: 


Simplifying
(x + 9.6)(3x + 0.9) = 0

Reorder the terms:
(9.6 + x)(3x + 0.9) = 0

Reorder the terms:
(9.6 + x)(0.9 + 3x) = 0

Multiply (9.6 + x) * (0.9 + 3x)
(9.6(0.9 + 3x) + x(0.9 + 3x)) = 0
((0.9 * 9.6 + 3x * 9.6) + x(0.9 + 3x)) = 0
((8.64 + 28.8x) + x(0.9 + 3x)) = 0
(8.64 + 28.8x + (0.9 * x + 3x * x)) = 0
(8.64 + 28.8x + (0.9x + 3x2)) = 0

Combine like terms: 28.8x + 0.9x = 29.7x
(8.64 + 29.7x + 3x2) = 0

Solving
8.64 + 29.7x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
2.88 + 9.9x + x2 = 0

Move the constant term to the right:

Add '-2.88' to each side of the equation.
2.88 + 9.9x + -2.88 + x2 = 0 + -2.88

Reorder the terms:
2.88 + -2.88 + 9.9x + x2 = 0 + -2.88

Combine like terms: 2.88 + -2.88 = 0.00
0.00 + 9.9x + x2 = 0 + -2.88
9.9x + x2 = 0 + -2.88

Combine like terms: 0 + -2.88 = -2.88
9.9x + x2 = -2.88

The x term is 9.9x.  Take half its coefficient (4.95).
Square it (24.5025) and add it to both sides.

Add '24.5025' to each side of the equation.
9.9x + 24.5025 + x2 = -2.88 + 24.5025

Reorder the terms:
24.5025 + 9.9x + x2 = -2.88 + 24.5025

Combine like terms: -2.88 + 24.5025 = 21.6225
24.5025 + 9.9x + x2 = 21.6225

Factor a perfect square on the left side:
(x + 4.95)(x + 4.95) = 21.6225

Calculate the square root of the right side: 4.65

Break this problem into two subproblems by setting 
(x + 4.95) equal to 4.65 and -4.65.


Subproblem 1
x + 4.95 = 4.65

Simplifying
x + 4.95 = 4.65

Reorder the terms:
4.95 + x = 4.65

Solving
4.95 + x = 4.65

Solving for variable 'x'.

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

Add '-4.95' to each side of the equation.
4.95 + -4.95 + x = 4.65 + -4.95

Combine like terms: 4.95 + -4.95 = 0.00
0.00 + x = 4.65 + -4.95
x = 4.65 + -4.95

Combine like terms: 4.65 + -4.95 = -0.3
x = -0.3

Simplifying
x = -0.3


Subproblem 2
x + 4.95 = -4.65

Simplifying
x + 4.95 = -4.65

Reorder the terms:
4.95 + x = -4.65

Solving
4.95 + x = -4.65

Solving for variable 'x'.

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

Add '-4.95' to each side of the equation.
4.95 + -4.95 + x = -4.65 + -4.95

Combine like terms: 4.95 + -4.95 = 0.00
0.00 + x = -4.65 + -4.95
x = -4.65 + -4.95

Combine like terms: -4.65 + -4.95 = -9.6
x = -9.6

Simplifying
x = -9.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.3, -9.6}

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