-7x(4x+2)-5(3x-9)=5(3x+6)

Solution for -7x(4x+2)-5(3x-9)=5(3x+6) equation:

Simplifying
-7x(4x + 2) + -5(3x + -9) = 5(3x + 6)

Reorder the terms:
-7x(2 + 4x) + -5(3x + -9) = 5(3x + 6)
(2 * -7x + 4x * -7x) + -5(3x + -9) = 5(3x + 6)
(-14x + -28x2) + -5(3x + -9) = 5(3x + 6)

Reorder the terms:
-14x + -28x2 + -5(-9 + 3x) = 5(3x + 6)
-14x + -28x2 + (-9 * -5 + 3x * -5) = 5(3x + 6)
-14x + -28x2 + (45 + -15x) = 5(3x + 6)

Reorder the terms:
45 + -14x + -15x + -28x2 = 5(3x + 6)

Combine like terms: -14x + -15x = -29x
45 + -29x + -28x2 = 5(3x + 6)

Reorder the terms:
45 + -29x + -28x2 = 5(6 + 3x)
45 + -29x + -28x2 = (6 * 5 + 3x * 5)
45 + -29x + -28x2 = (30 + 15x)

Solving
45 + -29x + -28x2 = 30 + 15x

Solving for variable 'x'.

Reorder the terms:
45 + -30 + -29x + -15x + -28x2 = 30 + 15x + -30 + -15x

Combine like terms: 45 + -30 = 15
15 + -29x + -15x + -28x2 = 30 + 15x + -30 + -15x

Combine like terms: -29x + -15x = -44x
15 + -44x + -28x2 = 30 + 15x + -30 + -15x

Reorder the terms:
15 + -44x + -28x2 = 30 + -30 + 15x + -15x

Combine like terms: 30 + -30 = 0
15 + -44x + -28x2 = 0 + 15x + -15x
15 + -44x + -28x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
15 + -44x + -28x2 = 0

Begin completing the square.  Divide all terms by
-28 the coefficient of the squared term: 

Divide each side by '-28'.
-0.5357142857 + 1.571428571x + x2 = 0

Move the constant term to the right:

Add '0.5357142857' to each side of the equation.
-0.5357142857 + 1.571428571x + 0.5357142857 + x2 = 0 + 0.5357142857

Reorder the terms:
-0.5357142857 + 0.5357142857 + 1.571428571x + x2 = 0 + 0.5357142857

Combine like terms: -0.5357142857 + 0.5357142857 = 0.0000000000
0.0000000000 + 1.571428571x + x2 = 0 + 0.5357142857
1.571428571x + x2 = 0 + 0.5357142857

Combine like terms: 0 + 0.5357142857 = 0.5357142857
1.571428571x + x2 = 0.5357142857

The x term is 1.571428571x.  Take half its coefficient (0.7857142855).
Square it (0.6173469384) and add it to both sides.

Add '0.6173469384' to each side of the equation.
1.571428571x + 0.6173469384 + x2 = 0.5357142857 + 0.6173469384

Reorder the terms:
0.6173469384 + 1.571428571x + x2 = 0.5357142857 + 0.6173469384

Combine like terms: 0.5357142857 + 0.6173469384 = 1.1530612241
0.6173469384 + 1.571428571x + x2 = 1.1530612241

Factor a perfect square on the left side:
(x + 0.7857142855)(x + 0.7857142855) = 1.1530612241

Calculate the square root of the right side: 1.073806884

Break this problem into two subproblems by setting 
(x + 0.7857142855) equal to 1.073806884 and -1.073806884.

Subproblem 1
x + 0.7857142855 = 1.073806884

Simplifying
x + 0.7857142855 = 1.073806884

Reorder the terms:
0.7857142855 + x = 1.073806884

Solving
0.7857142855 + x = 1.073806884

Solving for variable 'x'.

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

Add '-0.7857142855' to each side of the equation.
0.7857142855 + -0.7857142855 + x = 1.073806884 + -0.7857142855

Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000
0.0000000000 + x = 1.073806884 + -0.7857142855
x = 1.073806884 + -0.7857142855

Combine like terms: 1.073806884 + -0.7857142855 = 0.2880925985
x = 0.2880925985

Simplifying
x = 0.2880925985

Subproblem 2
x + 0.7857142855 = -1.073806884

Simplifying
x + 0.7857142855 = -1.073806884

Reorder the terms:
0.7857142855 + x = -1.073806884

Solving
0.7857142855 + x = -1.073806884

Solving for variable 'x'.

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

Add '-0.7857142855' to each side of the equation.
0.7857142855 + -0.7857142855 + x = -1.073806884 + -0.7857142855

Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000
0.0000000000 + x = -1.073806884 + -0.7857142855
x = -1.073806884 + -0.7857142855

Combine like terms: -1.073806884 + -0.7857142855 = -1.8595211695
x = -1.8595211695

Simplifying
x = -1.8595211695

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2880925985, -1.8595211695}