(5x+4)(3x-6)=x

Solution for (5x+4)(3x-6)=x equation:

Simplifying
(5x + 4)(3x + -6) = x

Reorder the terms:
(4 + 5x)(3x + -6) = x

Reorder the terms:
(4 + 5x)(-6 + 3x) = x

Multiply (4 + 5x) * (-6 + 3x)
(4(-6 + 3x) + 5x * (-6 + 3x)) = x
((-6 * 4 + 3x * 4) + 5x * (-6 + 3x)) = x
((-24 + 12x) + 5x * (-6 + 3x)) = x
(-24 + 12x + (-6 * 5x + 3x * 5x)) = x
(-24 + 12x + (-30x + 15x2)) = x

Combine like terms: 12x + -30x = -18x
(-24 + -18x + 15x2) = x

Solving
-24 + -18x + 15x2 = x

Solving for variable 'x'.

Reorder the terms:
-24 + -18x + -1x + 15x2 = x + -1x

Combine like terms: -18x + -1x = -19x
-24 + -19x + 15x2 = x + -1x

Combine like terms: x + -1x = 0
-24 + -19x + 15x2 = 0

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

Divide each side by '15'.
-1.6 + -1.266666667x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -1.266666667x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -1.266666667x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -1.266666667x + x2 = 0 + 1.6
-1.266666667x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-1.266666667x + x2 = 1.6

The x term is -1.266666667x.  Take half its coefficient (-0.6333333335).
Square it (0.4011111113) and add it to both sides.

Add '0.4011111113' to each side of the equation.
-1.266666667x + 0.4011111113 + x2 = 1.6 + 0.4011111113

Reorder the terms:
0.4011111113 + -1.266666667x + x2 = 1.6 + 0.4011111113

Combine like terms: 1.6 + 0.4011111113 = 2.0011111113
0.4011111113 + -1.266666667x + x2 = 2.0011111113

Factor a perfect square on the left side:
(x + -0.6333333335)(x + -0.6333333335) = 2.0011111113

Calculate the square root of the right side: 1.414606345

Break this problem into two subproblems by setting 
(x + -0.6333333335) equal to 1.414606345 and -1.414606345.

Subproblem 1
x + -0.6333333335 = 1.414606345

Simplifying
x + -0.6333333335 = 1.414606345

Reorder the terms:
-0.6333333335 + x = 1.414606345

Solving
-0.6333333335 + x = 1.414606345

Solving for variable 'x'.

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

Add '0.6333333335' to each side of the equation.
-0.6333333335 + 0.6333333335 + x = 1.414606345 + 0.6333333335

Combine like terms: -0.6333333335 + 0.6333333335 = 0.0000000000
0.0000000000 + x = 1.414606345 + 0.6333333335
x = 1.414606345 + 0.6333333335

Combine like terms: 1.414606345 + 0.6333333335 = 2.0479396785
x = 2.0479396785

Simplifying
x = 2.0479396785

Subproblem 2
x + -0.6333333335 = -1.414606345

Simplifying
x + -0.6333333335 = -1.414606345

Reorder the terms:
-0.6333333335 + x = -1.414606345

Solving
-0.6333333335 + x = -1.414606345

Solving for variable 'x'.

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

Add '0.6333333335' to each side of the equation.
-0.6333333335 + 0.6333333335 + x = -1.414606345 + 0.6333333335

Combine like terms: -0.6333333335 + 0.6333333335 = 0.0000000000
0.0000000000 + x = -1.414606345 + 0.6333333335
x = -1.414606345 + 0.6333333335

Combine like terms: -1.414606345 + 0.6333333335 = -0.7812730115
x = -0.7812730115

Simplifying
x = -0.7812730115

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.0479396785, -0.7812730115}