7x(2x-9)+(3x+8)-(5x+6)=5

Solution for 7x(2x-9)+(3x+8)-(5x+6)=5 equation:

Simplifying
7x(2x + -9) + (3x + 8) + -1(5x + 6) = 5

Reorder the terms:
7x(-9 + 2x) + (3x + 8) + -1(5x + 6) = 5
(-9 * 7x + 2x * 7x) + (3x + 8) + -1(5x + 6) = 5
(-63x + 14x2) + (3x + 8) + -1(5x + 6) = 5

Reorder the terms:
-63x + 14x2 + (8 + 3x) + -1(5x + 6) = 5

Remove parenthesis around (8 + 3x)
-63x + 14x2 + 8 + 3x + -1(5x + 6) = 5

Reorder the terms:
-63x + 14x2 + 8 + 3x + -1(6 + 5x) = 5
-63x + 14x2 + 8 + 3x + (6 * -1 + 5x * -1) = 5
-63x + 14x2 + 8 + 3x + (-6 + -5x) = 5

Reorder the terms:
8 + -6 + -63x + 3x + -5x + 14x2 = 5

Combine like terms: 8 + -6 = 2
2 + -63x + 3x + -5x + 14x2 = 5

Combine like terms: -63x + 3x = -60x
2 + -60x + -5x + 14x2 = 5

Combine like terms: -60x + -5x = -65x
2 + -65x + 14x2 = 5

Solving
2 + -65x + 14x2 = 5

Solving for variable 'x'.

Reorder the terms:
2 + -5 + -65x + 14x2 = 5 + -5

Combine like terms: 2 + -5 = -3
-3 + -65x + 14x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-3 + -65x + 14x2 = 0

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

Divide each side by '14'.
-0.2142857143 + -4.642857143x + x2 = 0

Move the constant term to the right:

Add '0.2142857143' to each side of the equation.
-0.2142857143 + -4.642857143x + 0.2142857143 + x2 = 0 + 0.2142857143

Reorder the terms:
-0.2142857143 + 0.2142857143 + -4.642857143x + x2 = 0 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + -4.642857143x + x2 = 0 + 0.2142857143
-4.642857143x + x2 = 0 + 0.2142857143

Combine like terms: 0 + 0.2142857143 = 0.2142857143
-4.642857143x + x2 = 0.2142857143

The x term is -4.642857143x.  Take half its coefficient (-2.321428572).
Square it (5.389030615) and add it to both sides.

Add '5.389030615' to each side of the equation.
-4.642857143x + 5.389030615 + x2 = 0.2142857143 + 5.389030615

Reorder the terms:
5.389030615 + -4.642857143x + x2 = 0.2142857143 + 5.389030615

Combine like terms: 0.2142857143 + 5.389030615 = 5.6033163293
5.389030615 + -4.642857143x + x2 = 5.6033163293

Factor a perfect square on the left side:
(x + -2.321428572)(x + -2.321428572) = 5.6033163293

Calculate the square root of the right side: 2.367132512

Break this problem into two subproblems by setting 
(x + -2.321428572) equal to 2.367132512 and -2.367132512.

Subproblem 1
x + -2.321428572 = 2.367132512

Simplifying
x + -2.321428572 = 2.367132512

Reorder the terms:
-2.321428572 + x = 2.367132512

Solving
-2.321428572 + x = 2.367132512

Solving for variable 'x'.

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

Add '2.321428572' to each side of the equation.
-2.321428572 + 2.321428572 + x = 2.367132512 + 2.321428572

Combine like terms: -2.321428572 + 2.321428572 = 0.000000000
0.000000000 + x = 2.367132512 + 2.321428572
x = 2.367132512 + 2.321428572

Combine like terms: 2.367132512 + 2.321428572 = 4.688561084
x = 4.688561084

Simplifying
x = 4.688561084

Subproblem 2
x + -2.321428572 = -2.367132512

Simplifying
x + -2.321428572 = -2.367132512

Reorder the terms:
-2.321428572 + x = -2.367132512

Solving
-2.321428572 + x = -2.367132512

Solving for variable 'x'.

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

Add '2.321428572' to each side of the equation.
-2.321428572 + 2.321428572 + x = -2.367132512 + 2.321428572

Combine like terms: -2.321428572 + 2.321428572 = 0.000000000
0.000000000 + x = -2.367132512 + 2.321428572
x = -2.367132512 + 2.321428572

Combine like terms: -2.367132512 + 2.321428572 = -0.04570394
x = -0.04570394

Simplifying
x = -0.04570394

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.688561084, -0.04570394}