4x(6x+9)=63

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Solution for 4x(6x+9)=63 equation: 


Simplifying
4x(6x + 9) = 63

Reorder the terms:
4x(9 + 6x) = 63
(9 * 4x + 6x * 4x) = 63
(36x + 24x2) = 63

Solving
36x + 24x2 = 63

Solving for variable 'x'.

Reorder the terms:
-63 + 36x + 24x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-63 + 36x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + 12x + 8x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-21 + 12x + 8x2)' equal to zero and attempt to solve:

Simplifying
-21 + 12x + 8x2 = 0

Solving
-21 + 12x + 8x2 = 0

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

Divide each side by '8'.
-2.625 + 1.5x + x2 = 0

Move the constant term to the right:

Add '2.625' to each side of the equation.
-2.625 + 1.5x + 2.625 + x2 = 0 + 2.625

Reorder the terms:
-2.625 + 2.625 + 1.5x + x2 = 0 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + 1.5x + x2 = 0 + 2.625
1.5x + x2 = 0 + 2.625

Combine like terms: 0 + 2.625 = 2.625
1.5x + x2 = 2.625

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 2.625 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 2.625 + 0.5625

Combine like terms: 2.625 + 0.5625 = 3.1875
0.5625 + 1.5x + x2 = 3.1875

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 3.1875

Calculate the square root of the right side: 1.785357107

Break this problem into two subproblems by setting 
(x + 0.75) equal to 1.785357107 and -1.785357107.


Subproblem 1
x + 0.75 = 1.785357107

Simplifying
x + 0.75 = 1.785357107

Reorder the terms:
0.75 + x = 1.785357107

Solving
0.75 + x = 1.785357107

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 1.785357107 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 1.785357107 + -0.75
x = 1.785357107 + -0.75

Combine like terms: 1.785357107 + -0.75 = 1.035357107
x = 1.035357107

Simplifying
x = 1.035357107


Subproblem 2
x + 0.75 = -1.785357107

Simplifying
x + 0.75 = -1.785357107

Reorder the terms:
0.75 + x = -1.785357107

Solving
0.75 + x = -1.785357107

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -1.785357107 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -1.785357107 + -0.75
x = -1.785357107 + -0.75

Combine like terms: -1.785357107 + -0.75 = -2.535357107
x = -2.535357107

Simplifying
x = -2.535357107


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.035357107, -2.535357107}
Solution
x = {1.035357107, -2.535357107}

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