x(3x-5)+(4x-2)=(7x+5)(x-2)

Solution for x(3x-5)+(4x-2)=(7x+5)(x-2) equation:

Simplifying
x(3x + -5) + (4x + -2) = (7x + 5)(x + -2)

Reorder the terms:
x(-5 + 3x) + (4x + -2) = (7x + 5)(x + -2)
(-5 * x + 3x * x) + (4x + -2) = (7x + 5)(x + -2)
(-5x + 3x2) + (4x + -2) = (7x + 5)(x + -2)

Reorder the terms:
-5x + 3x2 + (-2 + 4x) = (7x + 5)(x + -2)

Remove parenthesis around (-2 + 4x)
-5x + 3x2 + -2 + 4x = (7x + 5)(x + -2)

Reorder the terms:
-2 + -5x + 4x + 3x2 = (7x + 5)(x + -2)

Combine like terms: -5x + 4x = -1x
-2 + -1x + 3x2 = (7x + 5)(x + -2)

Reorder the terms:
-2 + -1x + 3x2 = (5 + 7x)(x + -2)

Reorder the terms:
-2 + -1x + 3x2 = (5 + 7x)(-2 + x)

Multiply (5 + 7x) * (-2 + x)
-2 + -1x + 3x2 = (5(-2 + x) + 7x * (-2 + x))
-2 + -1x + 3x2 = ((-2 * 5 + x * 5) + 7x * (-2 + x))
-2 + -1x + 3x2 = ((-10 + 5x) + 7x * (-2 + x))
-2 + -1x + 3x2 = (-10 + 5x + (-2 * 7x + x * 7x))
-2 + -1x + 3x2 = (-10 + 5x + (-14x + 7x2))

Combine like terms: 5x + -14x = -9x
-2 + -1x + 3x2 = (-10 + -9x + 7x2)

Solving
-2 + -1x + 3x2 = -10 + -9x + 7x2

Solving for variable 'x'.

Reorder the terms:
-2 + 10 + -1x + 9x + 3x2 + -7x2 = -10 + -9x + 7x2 + 10 + 9x + -7x2

Combine like terms: -2 + 10 = 8
8 + -1x + 9x + 3x2 + -7x2 = -10 + -9x + 7x2 + 10 + 9x + -7x2

Combine like terms: -1x + 9x = 8x
8 + 8x + 3x2 + -7x2 = -10 + -9x + 7x2 + 10 + 9x + -7x2

Combine like terms: 3x2 + -7x2 = -4x2
8 + 8x + -4x2 = -10 + -9x + 7x2 + 10 + 9x + -7x2

Reorder the terms:
8 + 8x + -4x2 = -10 + 10 + -9x + 9x + 7x2 + -7x2

Combine like terms: -10 + 10 = 0
8 + 8x + -4x2 = 0 + -9x + 9x + 7x2 + -7x2
8 + 8x + -4x2 = -9x + 9x + 7x2 + -7x2

Combine like terms: -9x + 9x = 0
8 + 8x + -4x2 = 0 + 7x2 + -7x2
8 + 8x + -4x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
8 + 8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 2x + -1x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + 2x + -1x2 = 0

Solving
2 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -2x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -2x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -2x + x2 = 0 + 2
-2x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-2x + x2 = 2

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 2 + 1

Reorder the terms:
1 + -2x + x2 = 2 + 1

Combine like terms: 2 + 1 = 3
1 + -2x + x2 = 3

Factor a perfect square on the left side:
(x + -1)(x + -1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -1) equal to 1.732050808 and -1.732050808.

Subproblem 1
x + -1 = 1.732050808

Simplifying
x + -1 = 1.732050808

Reorder the terms:
-1 + x = 1.732050808

Solving
-1 + x = 1.732050808

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.732050808 + 1
x = 1.732050808 + 1

Combine like terms: 1.732050808 + 1 = 2.732050808
x = 2.732050808

Simplifying
x = 2.732050808

Subproblem 2
x + -1 = -1.732050808

Simplifying
x + -1 = -1.732050808

Reorder the terms:
-1 + x = -1.732050808

Solving
-1 + x = -1.732050808

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.732050808 + 1
x = -1.732050808 + 1

Combine like terms: -1.732050808 + 1 = -0.732050808
x = -0.732050808

Simplifying
x = -0.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.732050808, -0.732050808}
Solution
x = {2.732050808, -0.732050808}