(7x+6)(x-2)=(6x-7)(x-3)

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

Simplifying
(7x + 6)(x + -2) = (6x + -7)(x + -3)

Reorder the terms:
(6 + 7x)(x + -2) = (6x + -7)(x + -3)

Reorder the terms:
(6 + 7x)(-2 + x) = (6x + -7)(x + -3)

Multiply (6 + 7x) * (-2 + x)
(6(-2 + x) + 7x * (-2 + x)) = (6x + -7)(x + -3)
((-2 * 6 + x * 6) + 7x * (-2 + x)) = (6x + -7)(x + -3)
((-12 + 6x) + 7x * (-2 + x)) = (6x + -7)(x + -3)
(-12 + 6x + (-2 * 7x + x * 7x)) = (6x + -7)(x + -3)
(-12 + 6x + (-14x + 7x2)) = (6x + -7)(x + -3)

Combine like terms: 6x + -14x = -8x
(-12 + -8x + 7x2) = (6x + -7)(x + -3)

Reorder the terms:
-12 + -8x + 7x2 = (-7 + 6x)(x + -3)

Reorder the terms:
-12 + -8x + 7x2 = (-7 + 6x)(-3 + x)

Multiply (-7 + 6x) * (-3 + x)
-12 + -8x + 7x2 = (-7(-3 + x) + 6x * (-3 + x))
-12 + -8x + 7x2 = ((-3 * -7 + x * -7) + 6x * (-3 + x))
-12 + -8x + 7x2 = ((21 + -7x) + 6x * (-3 + x))
-12 + -8x + 7x2 = (21 + -7x + (-3 * 6x + x * 6x))
-12 + -8x + 7x2 = (21 + -7x + (-18x + 6x2))

Combine like terms: -7x + -18x = -25x
-12 + -8x + 7x2 = (21 + -25x + 6x2)

Solving
-12 + -8x + 7x2 = 21 + -25x + 6x2

Solving for variable 'x'.

Reorder the terms:
-12 + -21 + -8x + 25x + 7x2 + -6x2 = 21 + -25x + 6x2 + -21 + 25x + -6x2

Combine like terms: -12 + -21 = -33
-33 + -8x + 25x + 7x2 + -6x2 = 21 + -25x + 6x2 + -21 + 25x + -6x2

Combine like terms: -8x + 25x = 17x
-33 + 17x + 7x2 + -6x2 = 21 + -25x + 6x2 + -21 + 25x + -6x2

Combine like terms: 7x2 + -6x2 = 1x2
-33 + 17x + 1x2 = 21 + -25x + 6x2 + -21 + 25x + -6x2

Reorder the terms:
-33 + 17x + 1x2 = 21 + -21 + -25x + 25x + 6x2 + -6x2

Combine like terms: 21 + -21 = 0
-33 + 17x + 1x2 = 0 + -25x + 25x + 6x2 + -6x2
-33 + 17x + 1x2 = -25x + 25x + 6x2 + -6x2

Combine like terms: -25x + 25x = 0
-33 + 17x + 1x2 = 0 + 6x2 + -6x2
-33 + 17x + 1x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-33 + 17x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + 17x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + 17x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + 17x + x2 = 0 + 33
17x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
17x + x2 = 33

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = 33 + 72.25

Reorder the terms:
72.25 + 17x + x2 = 33 + 72.25

Combine like terms: 33 + 72.25 = 105.25
72.25 + 17x + x2 = 105.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 105.25

Calculate the square root of the right side: 10.259142264

Break this problem into two subproblems by setting 
(x + 8.5) equal to 10.259142264 and -10.259142264.

Subproblem 1
x + 8.5 = 10.259142264

Simplifying
x + 8.5 = 10.259142264

Reorder the terms:
8.5 + x = 10.259142264

Solving
8.5 + x = 10.259142264

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 10.259142264 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 10.259142264 + -8.5
x = 10.259142264 + -8.5

Combine like terms: 10.259142264 + -8.5 = 1.759142264
x = 1.759142264

Simplifying
x = 1.759142264

Subproblem 2
x + 8.5 = -10.259142264

Simplifying
x + 8.5 = -10.259142264

Reorder the terms:
8.5 + x = -10.259142264

Solving
8.5 + x = -10.259142264

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = -10.259142264 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -10.259142264 + -8.5
x = -10.259142264 + -8.5

Combine like terms: -10.259142264 + -8.5 = -18.759142264
x = -18.759142264

Simplifying
x = -18.759142264

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.759142264, -18.759142264}