(9x^2+2x)(7)-(7x-8)(18x+2)=

Solution for (9x^2+2x)(7)-(7x-8)(18x+2)= equation:

Simplifying
(9x2 + 2x)(7) + -1(7x + -8)(18x + 2) = 0

Reorder the terms:
(2x + 9x2)(7) + -1(7x + -8)(18x + 2) = 0

Reorder the terms for easier multiplication:
7(2x + 9x2) + -1(7x + -8)(18x + 2) = 0
(2x * 7 + 9x2 * 7) + -1(7x + -8)(18x + 2) = 0
(14x + 63x2) + -1(7x + -8)(18x + 2) = 0

Reorder the terms:
14x + 63x2 + -1(-8 + 7x)(18x + 2) = 0

Reorder the terms:
14x + 63x2 + -1(-8 + 7x)(2 + 18x) = 0

Multiply (-8 + 7x) * (2 + 18x)
14x + 63x2 + -1(-8(2 + 18x) + 7x * (2 + 18x)) = 0
14x + 63x2 + -1((2 * -8 + 18x * -8) + 7x * (2 + 18x)) = 0
14x + 63x2 + -1((-16 + -144x) + 7x * (2 + 18x)) = 0
14x + 63x2 + -1(-16 + -144x + (2 * 7x + 18x * 7x)) = 0
14x + 63x2 + -1(-16 + -144x + (14x + 126x2)) = 0

Combine like terms: -144x + 14x = -130x
14x + 63x2 + -1(-16 + -130x + 126x2) = 0
14x + 63x2 + (-16 * -1 + -130x * -1 + 126x2 * -1) = 0
14x + 63x2 + (16 + 130x + -126x2) = 0

Reorder the terms:
16 + 14x + 130x + 63x2 + -126x2 = 0

Combine like terms: 14x + 130x = 144x
16 + 144x + 63x2 + -126x2 = 0

Combine like terms: 63x2 + -126x2 = -63x2
16 + 144x + -63x2 = 0

Solving
16 + 144x + -63x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-63 the coefficient of the squared term: 

Divide each side by '-63'.
-0.253968254 + -2.285714286x + x2 = 0

Move the constant term to the right:

Add '0.253968254' to each side of the equation.
-0.253968254 + -2.285714286x + 0.253968254 + x2 = 0 + 0.253968254

Reorder the terms:
-0.253968254 + 0.253968254 + -2.285714286x + x2 = 0 + 0.253968254

Combine like terms: -0.253968254 + 0.253968254 = 0.000000000
0.000000000 + -2.285714286x + x2 = 0 + 0.253968254
-2.285714286x + x2 = 0 + 0.253968254

Combine like terms: 0 + 0.253968254 = 0.253968254
-2.285714286x + x2 = 0.253968254

The x term is -2.285714286x.  Take half its coefficient (-1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
-2.285714286x + 1.306122449 + x2 = 0.253968254 + 1.306122449

Reorder the terms:
1.306122449 + -2.285714286x + x2 = 0.253968254 + 1.306122449

Combine like terms: 0.253968254 + 1.306122449 = 1.560090703
1.306122449 + -2.285714286x + x2 = 1.560090703

Factor a perfect square on the left side:
(x + -1.142857143)(x + -1.142857143) = 1.560090703

Calculate the square root of the right side: 1.249035909

Break this problem into two subproblems by setting 
(x + -1.142857143) equal to 1.249035909 and -1.249035909.

Subproblem 1
x + -1.142857143 = 1.249035909

Simplifying
x + -1.142857143 = 1.249035909

Reorder the terms:
-1.142857143 + x = 1.249035909

Solving
-1.142857143 + x = 1.249035909

Solving for variable 'x'.

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

Add '1.142857143' to each side of the equation.
-1.142857143 + 1.142857143 + x = 1.249035909 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = 1.249035909 + 1.142857143
x = 1.249035909 + 1.142857143

Combine like terms: 1.249035909 + 1.142857143 = 2.391893052
x = 2.391893052

Simplifying
x = 2.391893052

Subproblem 2
x + -1.142857143 = -1.249035909

Simplifying
x + -1.142857143 = -1.249035909

Reorder the terms:
-1.142857143 + x = -1.249035909

Solving
-1.142857143 + x = -1.249035909

Solving for variable 'x'.

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

Add '1.142857143' to each side of the equation.
-1.142857143 + 1.142857143 + x = -1.249035909 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + x = -1.249035909 + 1.142857143
x = -1.249035909 + 1.142857143

Combine like terms: -1.249035909 + 1.142857143 = -0.106178766
x = -0.106178766

Simplifying
x = -0.106178766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.391893052, -0.106178766}