7[2-(3+4x)]*-2x=-9+2(1-15x)

Solution for 7[2-(3+4x)]*-2x=-9+2(1-15x) equation:

Simplifying
7[2 + -1(3 + 4x)] * -2x = -9 + 2(1 + -15x)
7[2 + (3 * -1 + 4x * -1)] * -2x = -9 + 2(1 + -15x)
7[2 + (-3 + -4x)] * -2x = -9 + 2(1 + -15x)

Combine like terms: 2 + -3 = -1
7[-1 + -4x] * -2x = -9 + 2(1 + -15x)

Reorder the terms for easier multiplication:
7 * -2x[-1 + -4x] = -9 + 2(1 + -15x)

Multiply 7 * -2
-14x[-1 + -4x] = -9 + 2(1 + -15x)
[-1 * -14x + -4x * -14x] = -9 + 2(1 + -15x)
[14x + 56x2] = -9 + 2(1 + -15x)
14x + 56x2 = -9 + (1 * 2 + -15x * 2)
14x + 56x2 = -9 + (2 + -30x)

Combine like terms: -9 + 2 = -7
14x + 56x2 = -7 + -30x

Solving
14x + 56x2 = -7 + -30x

Solving for variable 'x'.

Reorder the terms:
7 + 14x + 30x + 56x2 = -7 + -30x + 7 + 30x

Combine like terms: 14x + 30x = 44x
7 + 44x + 56x2 = -7 + -30x + 7 + 30x

Reorder the terms:
7 + 44x + 56x2 = -7 + 7 + -30x + 30x

Combine like terms: -7 + 7 = 0
7 + 44x + 56x2 = 0 + -30x + 30x
7 + 44x + 56x2 = -30x + 30x

Combine like terms: -30x + 30x = 0
7 + 44x + 56x2 = 0

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

Divide each side by '56'.
0.125 + 0.7857142857x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 0.7857142857x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 0.7857142857x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 0.7857142857x + x2 = 0 + -0.125
0.7857142857x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
0.7857142857x + x2 = -0.125

The x term is 0.7857142857x.  Take half its coefficient (0.3928571429).
Square it (0.1543367347) and add it to both sides.

Add '0.1543367347' to each side of the equation.
0.7857142857x + 0.1543367347 + x2 = -0.125 + 0.1543367347

Reorder the terms:
0.1543367347 + 0.7857142857x + x2 = -0.125 + 0.1543367347

Combine like terms: -0.125 + 0.1543367347 = 0.0293367347
0.1543367347 + 0.7857142857x + x2 = 0.0293367347

Factor a perfect square on the left side:
(x + 0.3928571429)(x + 0.3928571429) = 0.0293367347

Calculate the square root of the right side: 0.171279697

Break this problem into two subproblems by setting 
(x + 0.3928571429) equal to 0.171279697 and -0.171279697.

Subproblem 1
x + 0.3928571429 = 0.171279697

Simplifying
x + 0.3928571429 = 0.171279697

Reorder the terms:
0.3928571429 + x = 0.171279697

Solving
0.3928571429 + x = 0.171279697

Solving for variable 'x'.

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

Add '-0.3928571429' to each side of the equation.
0.3928571429 + -0.3928571429 + x = 0.171279697 + -0.3928571429

Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000
0.0000000000 + x = 0.171279697 + -0.3928571429
x = 0.171279697 + -0.3928571429

Combine like terms: 0.171279697 + -0.3928571429 = -0.2215774459
x = -0.2215774459

Simplifying
x = -0.2215774459

Subproblem 2
x + 0.3928571429 = -0.171279697

Simplifying
x + 0.3928571429 = -0.171279697

Reorder the terms:
0.3928571429 + x = -0.171279697

Solving
0.3928571429 + x = -0.171279697

Solving for variable 'x'.

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

Add '-0.3928571429' to each side of the equation.
0.3928571429 + -0.3928571429 + x = -0.171279697 + -0.3928571429

Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000
0.0000000000 + x = -0.171279697 + -0.3928571429
x = -0.171279697 + -0.3928571429

Combine like terms: -0.171279697 + -0.3928571429 = -0.5641368399
x = -0.5641368399

Simplifying
x = -0.5641368399

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.2215774459, -0.5641368399}