5x(4x+6)-3(6x+2)=5(6x+6)-6(5x-2)

Solution for 5x(4x+6)-3(6x+2)=5(6x+6)-6(5x-2) equation:

Simplifying
5x(4x + 6) + -3(6x + 2) = 5(6x + 6) + -6(5x + -2)

Reorder the terms:
5x(6 + 4x) + -3(6x + 2) = 5(6x + 6) + -6(5x + -2)
(6 * 5x + 4x * 5x) + -3(6x + 2) = 5(6x + 6) + -6(5x + -2)
(30x + 20x2) + -3(6x + 2) = 5(6x + 6) + -6(5x + -2)

Reorder the terms:
30x + 20x2 + -3(2 + 6x) = 5(6x + 6) + -6(5x + -2)
30x + 20x2 + (2 * -3 + 6x * -3) = 5(6x + 6) + -6(5x + -2)
30x + 20x2 + (-6 + -18x) = 5(6x + 6) + -6(5x + -2)

Reorder the terms:
-6 + 30x + -18x + 20x2 = 5(6x + 6) + -6(5x + -2)

Combine like terms: 30x + -18x = 12x
-6 + 12x + 20x2 = 5(6x + 6) + -6(5x + -2)

Reorder the terms:
-6 + 12x + 20x2 = 5(6 + 6x) + -6(5x + -2)
-6 + 12x + 20x2 = (6 * 5 + 6x * 5) + -6(5x + -2)
-6 + 12x + 20x2 = (30 + 30x) + -6(5x + -2)

Reorder the terms:
-6 + 12x + 20x2 = 30 + 30x + -6(-2 + 5x)
-6 + 12x + 20x2 = 30 + 30x + (-2 * -6 + 5x * -6)
-6 + 12x + 20x2 = 30 + 30x + (12 + -30x)

Reorder the terms:
-6 + 12x + 20x2 = 30 + 12 + 30x + -30x

Combine like terms: 30 + 12 = 42
-6 + 12x + 20x2 = 42 + 30x + -30x

Combine like terms: 30x + -30x = 0
-6 + 12x + 20x2 = 42 + 0
-6 + 12x + 20x2 = 42

Solving
-6 + 12x + 20x2 = 42

Solving for variable 'x'.

Reorder the terms:
-6 + -42 + 12x + 20x2 = 42 + -42

Combine like terms: -6 + -42 = -48
-48 + 12x + 20x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-48 + 12x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + 3x + 5x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-12 + 3x + 5x2)' equal to zero and attempt to solve:

Simplifying
-12 + 3x + 5x2 = 0

Solving
-12 + 3x + 5x2 = 0

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

Divide each side by '5'.
-2.4 + 0.6x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 0.6x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 0.6x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 0.6x + x2 = 0 + 2.4
0.6x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
0.6x + x2 = 2.4

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 2.4 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 2.4 + 0.09

Combine like terms: 2.4 + 0.09 = 2.49
0.09 + 0.6x + x2 = 2.49

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 2.49

Calculate the square root of the right side: 1.577973384

Break this problem into two subproblems by setting 
(x + 0.3) equal to 1.577973384 and -1.577973384.

Subproblem 1
x + 0.3 = 1.577973384

Simplifying
x + 0.3 = 1.577973384

Reorder the terms:
0.3 + x = 1.577973384

Solving
0.3 + x = 1.577973384

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = 1.577973384 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 1.577973384 + -0.3
x = 1.577973384 + -0.3

Combine like terms: 1.577973384 + -0.3 = 1.277973384
x = 1.277973384

Simplifying
x = 1.277973384

Subproblem 2
x + 0.3 = -1.577973384

Simplifying
x + 0.3 = -1.577973384

Reorder the terms:
0.3 + x = -1.577973384

Solving
0.3 + x = -1.577973384

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = -1.577973384 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -1.577973384 + -0.3
x = -1.577973384 + -0.3

Combine like terms: -1.577973384 + -0.3 = -1.877973384
x = -1.877973384

Simplifying
x = -1.877973384

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.277973384, -1.877973384}
Solution
x = {1.277973384, -1.877973384}