(6x+4)(x-4)=9

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


Simplifying
(6x + 4)(x + -4) = 9

Reorder the terms:
(4 + 6x)(x + -4) = 9

Reorder the terms:
(4 + 6x)(-4 + x) = 9

Multiply (4 + 6x) * (-4 + x)
(4(-4 + x) + 6x * (-4 + x)) = 9
((-4 * 4 + x * 4) + 6x * (-4 + x)) = 9
((-16 + 4x) + 6x * (-4 + x)) = 9
(-16 + 4x + (-4 * 6x + x * 6x)) = 9
(-16 + 4x + (-24x + 6x2)) = 9

Combine like terms: 4x + -24x = -20x
(-16 + -20x + 6x2) = 9

Solving
-16 + -20x + 6x2 = 9

Solving for variable 'x'.

Reorder the terms:
-16 + -9 + -20x + 6x2 = 9 + -9

Combine like terms: -16 + -9 = -25
-25 + -20x + 6x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-25 + -20x + 6x2 = 0

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

Divide each side by '6'.
-4.166666667 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '4.166666667' to each side of the equation.
-4.166666667 + -3.333333333x + 4.166666667 + x2 = 0 + 4.166666667

Reorder the terms:
-4.166666667 + 4.166666667 + -3.333333333x + x2 = 0 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + -3.333333333x + x2 = 0 + 4.166666667
-3.333333333x + x2 = 0 + 4.166666667

Combine like terms: 0 + 4.166666667 = 4.166666667
-3.333333333x + x2 = 4.166666667

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 4.166666667 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 4.166666667 + 2.777777779

Combine like terms: 4.166666667 + 2.777777779 = 6.944444446
2.777777779 + -3.333333333x + x2 = 6.944444446

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 6.944444446

Calculate the square root of the right side: 2.635231384

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 2.635231384 and -2.635231384.

Subproblem 1

x + -1.666666667 = 2.635231384 Simplifying x + -1.666666667 = 2.635231384 Reorder the terms: -1.666666667 + x = 2.635231384 Solving -1.666666667 + x = 2.635231384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 2.635231384 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 2.635231384 + 1.666666667 x = 2.635231384 + 1.666666667 Combine like terms: 2.635231384 + 1.666666667 = 4.301898051 x = 4.301898051 Simplifying x = 4.301898051

Subproblem 2

x + -1.666666667 = -2.635231384 Simplifying x + -1.666666667 = -2.635231384 Reorder the terms: -1.666666667 + x = -2.635231384 Solving -1.666666667 + x = -2.635231384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -2.635231384 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -2.635231384 + 1.666666667 x = -2.635231384 + 1.666666667 Combine like terms: -2.635231384 + 1.666666667 = -0.968564717 x = -0.968564717 Simplifying x = -0.968564717

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.301898051, -0.968564717}

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