-32+6(3x+4)=-(-5x+38)3x

Solution for -32+6(3x+4)=-(-5x+38)3x equation:

Simplifying
-32 + 6(3x + 4) = -1(-5x + 38) * 3x

Reorder the terms:
-32 + 6(4 + 3x) = -1(-5x + 38) * 3x
-32 + (4 * 6 + 3x * 6) = -1(-5x + 38) * 3x
-32 + (24 + 18x) = -1(-5x + 38) * 3x

Combine like terms: -32 + 24 = -8
-8 + 18x = -1(-5x + 38) * 3x

Reorder the terms:
-8 + 18x = -1(38 + -5x) * 3x

Reorder the terms for easier multiplication:
-8 + 18x = -1 * 3x(38 + -5x)

Multiply -1 * 3
-8 + 18x = -3x(38 + -5x)
-8 + 18x = (38 * -3x + -5x * -3x)
-8 + 18x = (-114x + 15x2)

Solving
-8 + 18x = -114x + 15x2

Solving for variable 'x'.

Combine like terms: 18x + 114x = 132x
-8 + 132x + -15x2 = -114x + 15x2 + 114x + -15x2

Reorder the terms:
-8 + 132x + -15x2 = -114x + 114x + 15x2 + -15x2

Combine like terms: -114x + 114x = 0
-8 + 132x + -15x2 = 0 + 15x2 + -15x2
-8 + 132x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-8 + 132x + -15x2 = 0

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

Divide each side by '-15'.
0.5333333333 + -8.8x + x2 = 0

Move the constant term to the right:

Add '-0.5333333333' to each side of the equation.
0.5333333333 + -8.8x + -0.5333333333 + x2 = 0 + -0.5333333333

Reorder the terms:
0.5333333333 + -0.5333333333 + -8.8x + x2 = 0 + -0.5333333333

Combine like terms: 0.5333333333 + -0.5333333333 = 0.0000000000
0.0000000000 + -8.8x + x2 = 0 + -0.5333333333
-8.8x + x2 = 0 + -0.5333333333

Combine like terms: 0 + -0.5333333333 = -0.5333333333
-8.8x + x2 = -0.5333333333

The x term is -8.8x.  Take half its coefficient (-4.4).
Square it (19.36) and add it to both sides.

Add '19.36' to each side of the equation.
-8.8x + 19.36 + x2 = -0.5333333333 + 19.36

Reorder the terms:
19.36 + -8.8x + x2 = -0.5333333333 + 19.36

Combine like terms: -0.5333333333 + 19.36 = 18.8266666667
19.36 + -8.8x + x2 = 18.8266666667

Factor a perfect square on the left side:
(x + -4.4)(x + -4.4) = 18.8266666667

Calculate the square root of the right side: 4.338970692

Break this problem into two subproblems by setting 
(x + -4.4) equal to 4.338970692 and -4.338970692.

Subproblem 1
x + -4.4 = 4.338970692

Simplifying
x + -4.4 = 4.338970692

Reorder the terms:
-4.4 + x = 4.338970692

Solving
-4.4 + x = 4.338970692

Solving for variable 'x'.

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

Add '4.4' to each side of the equation.
-4.4 + 4.4 + x = 4.338970692 + 4.4

Combine like terms: -4.4 + 4.4 = 0.0
0.0 + x = 4.338970692 + 4.4
x = 4.338970692 + 4.4

Combine like terms: 4.338970692 + 4.4 = 8.738970692
x = 8.738970692

Simplifying
x = 8.738970692

Subproblem 2
x + -4.4 = -4.338970692

Simplifying
x + -4.4 = -4.338970692

Reorder the terms:
-4.4 + x = -4.338970692

Solving
-4.4 + x = -4.338970692

Solving for variable 'x'.

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

Add '4.4' to each side of the equation.
-4.4 + 4.4 + x = -4.338970692 + 4.4

Combine like terms: -4.4 + 4.4 = 0.0
0.0 + x = -4.338970692 + 4.4
x = -4.338970692 + 4.4

Combine like terms: -4.338970692 + 4.4 = 0.061029308
x = 0.061029308

Simplifying
x = 0.061029308

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.738970692, 0.061029308}