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

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

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

Reorder the terms:
3(-2 + 5x) * 6x = 3(3x + 2)

Reorder the terms for easier multiplication:
3 * 6x(-2 + 5x) = 3(3x + 2)

Multiply 3 * 6
18x(-2 + 5x) = 3(3x + 2)
(-2 * 18x + 5x * 18x) = 3(3x + 2)
(-36x + 90x2) = 3(3x + 2)

Reorder the terms:
-36x + 90x2 = 3(2 + 3x)
-36x + 90x2 = (2 * 3 + 3x * 3)
-36x + 90x2 = (6 + 9x)

Solving
-36x + 90x2 = 6 + 9x

Solving for variable 'x'.

Reorder the terms:
-6 + -36x + -9x + 90x2 = 6 + 9x + -6 + -9x

Combine like terms: -36x + -9x = -45x
-6 + -45x + 90x2 = 6 + 9x + -6 + -9x

Reorder the terms:
-6 + -45x + 90x2 = 6 + -6 + 9x + -9x

Combine like terms: 6 + -6 = 0
-6 + -45x + 90x2 = 0 + 9x + -9x
-6 + -45x + 90x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-6 + -45x + 90x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -15x + 30x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -15x + 30x2)' equal to zero and attempt to solve:

Simplifying
-2 + -15x + 30x2 = 0

Solving
-2 + -15x + 30x2 = 0

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

Divide each side by '30'.
-0.06666666667 + -0.5x + x2 = 0.0

Move the constant term to the right:

Add '0.06666666667' to each side of the equation.
-0.06666666667 + -0.5x + 0.06666666667 + x2 = 0.0 + 0.06666666667

Reorder the terms:
-0.06666666667 + 0.06666666667 + -0.5x + x2 = 0.0 + 0.06666666667

Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000
0.00000000000 + -0.5x + x2 = 0.0 + 0.06666666667
-0.5x + x2 = 0.0 + 0.06666666667

Combine like terms: 0.0 + 0.06666666667 = 0.06666666667
-0.5x + x2 = 0.06666666667

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.06666666667 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.06666666667 + 0.0625

Combine like terms: 0.06666666667 + 0.0625 = 0.12916666667
0.0625 + -0.5x + x2 = 0.12916666667

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.12916666667

Calculate the square root of the right side: 0.359397644

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.359397644 and -0.359397644.

Subproblem 1
x + -0.25 = 0.359397644

Simplifying
x + -0.25 = 0.359397644

Reorder the terms:
-0.25 + x = 0.359397644

Solving
-0.25 + x = 0.359397644

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 0.359397644 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.359397644 + 0.25
x = 0.359397644 + 0.25

Combine like terms: 0.359397644 + 0.25 = 0.609397644
x = 0.609397644

Simplifying
x = 0.609397644

Subproblem 2
x + -0.25 = -0.359397644

Simplifying
x + -0.25 = -0.359397644

Reorder the terms:
-0.25 + x = -0.359397644

Solving
-0.25 + x = -0.359397644

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -0.359397644 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -0.359397644 + 0.25
x = -0.359397644 + 0.25

Combine like terms: -0.359397644 + 0.25 = -0.109397644
x = -0.109397644

Simplifying
x = -0.109397644

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.609397644, -0.109397644}
Solution
x = {0.609397644, -0.109397644}