(2x+1)(7x*9-9+3)+4-7=49

Solution for (2x+1)(7x*9-9+3)+4-7=49 equation:

Simplifying
(2x + 1)(7x * 9 + -9 + 3) + 4 + -7 = 49

Reorder the terms:
(1 + 2x)(7x * 9 + -9 + 3) + 4 + -7 = 49

Reorder the terms for easier multiplication:
(1 + 2x)(7 * 9x + -9 + 3) + 4 + -7 = 49

Multiply 7 * 9
(1 + 2x)(63x + -9 + 3) + 4 + -7 = 49

Reorder the terms:
(1 + 2x)(-9 + 3 + 63x) + 4 + -7 = 49

Combine like terms: -9 + 3 = -6
(1 + 2x)(-6 + 63x) + 4 + -7 = 49

Multiply (1 + 2x) * (-6 + 63x)
(1(-6 + 63x) + 2x * (-6 + 63x)) + 4 + -7 = 49
((-6 * 1 + 63x * 1) + 2x * (-6 + 63x)) + 4 + -7 = 49
((-6 + 63x) + 2x * (-6 + 63x)) + 4 + -7 = 49
(-6 + 63x + (-6 * 2x + 63x * 2x)) + 4 + -7 = 49
(-6 + 63x + (-12x + 126x2)) + 4 + -7 = 49

Combine like terms: 63x + -12x = 51x
(-6 + 51x + 126x2) + 4 + -7 = 49

Reorder the terms:
-6 + 4 + -7 + 51x + 126x2 = 49

Combine like terms: -6 + 4 = -2
-2 + -7 + 51x + 126x2 = 49

Combine like terms: -2 + -7 = -9
-9 + 51x + 126x2 = 49

Solving
-9 + 51x + 126x2 = 49

Solving for variable 'x'.

Reorder the terms:
-9 + -49 + 51x + 126x2 = 49 + -49

Combine like terms: -9 + -49 = -58
-58 + 51x + 126x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-58 + 51x + 126x2 = 0

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

Divide each side by '126'.
-0.4603174603 + 0.4047619048x + x2 = 0

Move the constant term to the right:

Add '0.4603174603' to each side of the equation.
-0.4603174603 + 0.4047619048x + 0.4603174603 + x2 = 0 + 0.4603174603

Reorder the terms:
-0.4603174603 + 0.4603174603 + 0.4047619048x + x2 = 0 + 0.4603174603

Combine like terms: -0.4603174603 + 0.4603174603 = 0.0000000000
0.0000000000 + 0.4047619048x + x2 = 0 + 0.4603174603
0.4047619048x + x2 = 0 + 0.4603174603

Combine like terms: 0 + 0.4603174603 = 0.4603174603
0.4047619048x + x2 = 0.4603174603

The x term is 0.4047619048x.  Take half its coefficient (0.2023809524).
Square it (0.04095804989) and add it to both sides.

Add '0.04095804989' to each side of the equation.
0.4047619048x + 0.04095804989 + x2 = 0.4603174603 + 0.04095804989

Reorder the terms:
0.04095804989 + 0.4047619048x + x2 = 0.4603174603 + 0.04095804989

Combine like terms: 0.4603174603 + 0.04095804989 = 0.50127551019
0.04095804989 + 0.4047619048x + x2 = 0.50127551019

Factor a perfect square on the left side:
(x + 0.2023809524)(x + 0.2023809524) = 0.50127551019

Calculate the square root of the right side: 0.708008129

Break this problem into two subproblems by setting 
(x + 0.2023809524) equal to 0.708008129 and -0.708008129.

Subproblem 1
x + 0.2023809524 = 0.708008129

Simplifying
x + 0.2023809524 = 0.708008129

Reorder the terms:
0.2023809524 + x = 0.708008129

Solving
0.2023809524 + x = 0.708008129

Solving for variable 'x'.

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

Add '-0.2023809524' to each side of the equation.
0.2023809524 + -0.2023809524 + x = 0.708008129 + -0.2023809524

Combine like terms: 0.2023809524 + -0.2023809524 = 0.0000000000
0.0000000000 + x = 0.708008129 + -0.2023809524
x = 0.708008129 + -0.2023809524

Combine like terms: 0.708008129 + -0.2023809524 = 0.5056271766
x = 0.5056271766

Simplifying
x = 0.5056271766

Subproblem 2
x + 0.2023809524 = -0.708008129

Simplifying
x + 0.2023809524 = -0.708008129

Reorder the terms:
0.2023809524 + x = -0.708008129

Solving
0.2023809524 + x = -0.708008129

Solving for variable 'x'.

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

Add '-0.2023809524' to each side of the equation.
0.2023809524 + -0.2023809524 + x = -0.708008129 + -0.2023809524

Combine like terms: 0.2023809524 + -0.2023809524 = 0.0000000000
0.0000000000 + x = -0.708008129 + -0.2023809524
x = -0.708008129 + -0.2023809524

Combine like terms: -0.708008129 + -0.2023809524 = -0.9103890814
x = -0.9103890814

Simplifying
x = -0.9103890814

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5056271766, -0.9103890814}