2(x-5)(x-7)=5x^2-41x+46

Solution for 2(x-5)(x-7)=5x^2-41x+46 equation:

Simplifying
2(x + -5)(x + -7) = 5x2 + -41x + 46

Reorder the terms:
2(-5 + x)(x + -7) = 5x2 + -41x + 46

Reorder the terms:
2(-5 + x)(-7 + x) = 5x2 + -41x + 46

Multiply (-5 + x) * (-7 + x)
2(-5(-7 + x) + x(-7 + x)) = 5x2 + -41x + 46
2((-7 * -5 + x * -5) + x(-7 + x)) = 5x2 + -41x + 46
2((35 + -5x) + x(-7 + x)) = 5x2 + -41x + 46
2(35 + -5x + (-7 * x + x * x)) = 5x2 + -41x + 46
2(35 + -5x + (-7x + x2)) = 5x2 + -41x + 46

Combine like terms: -5x + -7x = -12x
2(35 + -12x + x2) = 5x2 + -41x + 46
(35 * 2 + -12x * 2 + x2 * 2) = 5x2 + -41x + 46
(70 + -24x + 2x2) = 5x2 + -41x + 46

Reorder the terms:
70 + -24x + 2x2 = 46 + -41x + 5x2

Solving
70 + -24x + 2x2 = 46 + -41x + 5x2

Solving for variable 'x'.

Reorder the terms:
70 + -46 + -24x + 41x + 2x2 + -5x2 = 46 + -41x + 5x2 + -46 + 41x + -5x2

Combine like terms: 70 + -46 = 24
24 + -24x + 41x + 2x2 + -5x2 = 46 + -41x + 5x2 + -46 + 41x + -5x2

Combine like terms: -24x + 41x = 17x
24 + 17x + 2x2 + -5x2 = 46 + -41x + 5x2 + -46 + 41x + -5x2

Combine like terms: 2x2 + -5x2 = -3x2
24 + 17x + -3x2 = 46 + -41x + 5x2 + -46 + 41x + -5x2

Reorder the terms:
24 + 17x + -3x2 = 46 + -46 + -41x + 41x + 5x2 + -5x2

Combine like terms: 46 + -46 = 0
24 + 17x + -3x2 = 0 + -41x + 41x + 5x2 + -5x2
24 + 17x + -3x2 = -41x + 41x + 5x2 + -5x2

Combine like terms: -41x + 41x = 0
24 + 17x + -3x2 = 0 + 5x2 + -5x2
24 + 17x + -3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
24 + 17x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-8 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -5.666666667x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -5.666666667x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5.666666667x + x2 = 0 + 8
-5.666666667x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-5.666666667x + x2 = 8

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = 8 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = 8 + 8.027777782

Combine like terms: 8 + 8.027777782 = 16.027777782
8.027777782 + -5.666666667x + x2 = 16.027777782

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 16.027777782

Calculate the square root of the right side: 4.003470717

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 4.003470717 and -4.003470717.

Subproblem 1
x + -2.833333334 = 4.003470717

Simplifying
x + -2.833333334 = 4.003470717

Reorder the terms:
-2.833333334 + x = 4.003470717

Solving
-2.833333334 + x = 4.003470717

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = 4.003470717 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = 4.003470717 + 2.833333334
x = 4.003470717 + 2.833333334

Combine like terms: 4.003470717 + 2.833333334 = 6.836804051
x = 6.836804051

Simplifying
x = 6.836804051

Subproblem 2
x + -2.833333334 = -4.003470717

Simplifying
x + -2.833333334 = -4.003470717

Reorder the terms:
-2.833333334 + x = -4.003470717

Solving
-2.833333334 + x = -4.003470717

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = -4.003470717 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = -4.003470717 + 2.833333334
x = -4.003470717 + 2.833333334

Combine like terms: -4.003470717 + 2.833333334 = -1.170137383
x = -1.170137383

Simplifying
x = -1.170137383

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.836804051, -1.170137383}