5(3-2x)3x=-6-7(x-3)

Solution for 5(3-2x)3x=-6-7(x-3) equation:

Simplifying
5(3 + -2x) * 3x = -6 + -7(x + -3)

Reorder the terms for easier multiplication:
5 * 3x(3 + -2x) = -6 + -7(x + -3)

Multiply 5 * 3
15x(3 + -2x) = -6 + -7(x + -3)
(3 * 15x + -2x * 15x) = -6 + -7(x + -3)
(45x + -30x2) = -6 + -7(x + -3)

Reorder the terms:
45x + -30x2 = -6 + -7(-3 + x)
45x + -30x2 = -6 + (-3 * -7 + x * -7)
45x + -30x2 = -6 + (21 + -7x)

Combine like terms: -6 + 21 = 15
45x + -30x2 = 15 + -7x

Solving
45x + -30x2 = 15 + -7x

Solving for variable 'x'.

Reorder the terms:
-15 + 45x + 7x + -30x2 = 15 + -7x + -15 + 7x

Combine like terms: 45x + 7x = 52x
-15 + 52x + -30x2 = 15 + -7x + -15 + 7x

Reorder the terms:
-15 + 52x + -30x2 = 15 + -15 + -7x + 7x

Combine like terms: 15 + -15 = 0
-15 + 52x + -30x2 = 0 + -7x + 7x
-15 + 52x + -30x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-15 + 52x + -30x2 = 0

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

Divide each side by '-30'.
0.5 + -1.733333333x + x2 = 0.0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -1.733333333x + -0.5 + x2 = 0.0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1.733333333x + x2 = 0.0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1.733333333x + x2 = 0.0 + -0.5
-1.733333333x + x2 = 0.0 + -0.5

Combine like terms: 0.0 + -0.5 = -0.5
-1.733333333x + x2 = -0.5

The x term is -1.733333333x.  Take half its coefficient (-0.8666666665).
Square it (0.7511111108) and add it to both sides.

Add '0.7511111108' to each side of the equation.
-1.733333333x + 0.7511111108 + x2 = -0.5 + 0.7511111108

Reorder the terms:
0.7511111108 + -1.733333333x + x2 = -0.5 + 0.7511111108

Combine like terms: -0.5 + 0.7511111108 = 0.2511111108
0.7511111108 + -1.733333333x + x2 = 0.2511111108

Factor a perfect square on the left side:
(x + -0.8666666665)(x + -0.8666666665) = 0.2511111108

Calculate the square root of the right side: 0.501109879

Break this problem into two subproblems by setting 
(x + -0.8666666665) equal to 0.501109879 and -0.501109879.

Subproblem 1
x + -0.8666666665 = 0.501109879

Simplifying
x + -0.8666666665 = 0.501109879

Reorder the terms:
-0.8666666665 + x = 0.501109879

Solving
-0.8666666665 + x = 0.501109879

Solving for variable 'x'.

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

Add '0.8666666665' to each side of the equation.
-0.8666666665 + 0.8666666665 + x = 0.501109879 + 0.8666666665

Combine like terms: -0.8666666665 + 0.8666666665 = 0.0000000000
0.0000000000 + x = 0.501109879 + 0.8666666665
x = 0.501109879 + 0.8666666665

Combine like terms: 0.501109879 + 0.8666666665 = 1.3677765455
x = 1.3677765455

Simplifying
x = 1.3677765455

Subproblem 2
x + -0.8666666665 = -0.501109879

Simplifying
x + -0.8666666665 = -0.501109879

Reorder the terms:
-0.8666666665 + x = -0.501109879

Solving
-0.8666666665 + x = -0.501109879

Solving for variable 'x'.

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

Add '0.8666666665' to each side of the equation.
-0.8666666665 + 0.8666666665 + x = -0.501109879 + 0.8666666665

Combine like terms: -0.8666666665 + 0.8666666665 = 0.0000000000
0.0000000000 + x = -0.501109879 + 0.8666666665
x = -0.501109879 + 0.8666666665

Combine like terms: -0.501109879 + 0.8666666665 = 0.3655567875
x = 0.3655567875

Simplifying
x = 0.3655567875

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3677765455, 0.3655567875}