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

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

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

Reorder the terms:
(5 + x)(x + 7) = (3x + 8)(x + -9)

Reorder the terms:
(5 + x)(7 + x) = (3x + 8)(x + -9)

Multiply (5 + x) * (7 + x)
(5(7 + x) + x(7 + x)) = (3x + 8)(x + -9)
((7 * 5 + x * 5) + x(7 + x)) = (3x + 8)(x + -9)
((35 + 5x) + x(7 + x)) = (3x + 8)(x + -9)
(35 + 5x + (7 * x + x * x)) = (3x + 8)(x + -9)
(35 + 5x + (7x + x2)) = (3x + 8)(x + -9)

Combine like terms: 5x + 7x = 12x
(35 + 12x + x2) = (3x + 8)(x + -9)

Reorder the terms:
35 + 12x + x2 = (8 + 3x)(x + -9)

Reorder the terms:
35 + 12x + x2 = (8 + 3x)(-9 + x)

Multiply (8 + 3x) * (-9 + x)
35 + 12x + x2 = (8(-9 + x) + 3x * (-9 + x))
35 + 12x + x2 = ((-9 * 8 + x * 8) + 3x * (-9 + x))
35 + 12x + x2 = ((-72 + 8x) + 3x * (-9 + x))
35 + 12x + x2 = (-72 + 8x + (-9 * 3x + x * 3x))
35 + 12x + x2 = (-72 + 8x + (-27x + 3x2))

Combine like terms: 8x + -27x = -19x
35 + 12x + x2 = (-72 + -19x + 3x2)

Solving
35 + 12x + x2 = -72 + -19x + 3x2

Solving for variable 'x'.

Reorder the terms:
35 + 72 + 12x + 19x + x2 + -3x2 = -72 + -19x + 3x2 + 72 + 19x + -3x2

Combine like terms: 35 + 72 = 107
107 + 12x + 19x + x2 + -3x2 = -72 + -19x + 3x2 + 72 + 19x + -3x2

Combine like terms: 12x + 19x = 31x
107 + 31x + x2 + -3x2 = -72 + -19x + 3x2 + 72 + 19x + -3x2

Combine like terms: x2 + -3x2 = -2x2
107 + 31x + -2x2 = -72 + -19x + 3x2 + 72 + 19x + -3x2

Reorder the terms:
107 + 31x + -2x2 = -72 + 72 + -19x + 19x + 3x2 + -3x2

Combine like terms: -72 + 72 = 0
107 + 31x + -2x2 = 0 + -19x + 19x + 3x2 + -3x2
107 + 31x + -2x2 = -19x + 19x + 3x2 + -3x2

Combine like terms: -19x + 19x = 0
107 + 31x + -2x2 = 0 + 3x2 + -3x2
107 + 31x + -2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
107 + 31x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-53.5 + -15.5x + x2 = 0

Move the constant term to the right:

Add '53.5' to each side of the equation.
-53.5 + -15.5x + 53.5 + x2 = 0 + 53.5

Reorder the terms:
-53.5 + 53.5 + -15.5x + x2 = 0 + 53.5

Combine like terms: -53.5 + 53.5 = 0.0
0.0 + -15.5x + x2 = 0 + 53.5
-15.5x + x2 = 0 + 53.5

Combine like terms: 0 + 53.5 = 53.5
-15.5x + x2 = 53.5

The x term is -15.5x.  Take half its coefficient (-7.75).
Square it (60.0625) and add it to both sides.

Add '60.0625' to each side of the equation.
-15.5x + 60.0625 + x2 = 53.5 + 60.0625

Reorder the terms:
60.0625 + -15.5x + x2 = 53.5 + 60.0625

Combine like terms: 53.5 + 60.0625 = 113.5625
60.0625 + -15.5x + x2 = 113.5625

Factor a perfect square on the left side:
(x + -7.75)(x + -7.75) = 113.5625

Calculate the square root of the right side: 10.656570743

Break this problem into two subproblems by setting 
(x + -7.75) equal to 10.656570743 and -10.656570743.

Subproblem 1
x + -7.75 = 10.656570743

Simplifying
x + -7.75 = 10.656570743

Reorder the terms:
-7.75 + x = 10.656570743

Solving
-7.75 + x = 10.656570743

Solving for variable 'x'.

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

Add '7.75' to each side of the equation.
-7.75 + 7.75 + x = 10.656570743 + 7.75

Combine like terms: -7.75 + 7.75 = 0.00
0.00 + x = 10.656570743 + 7.75
x = 10.656570743 + 7.75

Combine like terms: 10.656570743 + 7.75 = 18.406570743
x = 18.406570743

Simplifying
x = 18.406570743

Subproblem 2
x + -7.75 = -10.656570743

Simplifying
x + -7.75 = -10.656570743

Reorder the terms:
-7.75 + x = -10.656570743

Solving
-7.75 + x = -10.656570743

Solving for variable 'x'.

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

Add '7.75' to each side of the equation.
-7.75 + 7.75 + x = -10.656570743 + 7.75

Combine like terms: -7.75 + 7.75 = 0.00
0.00 + x = -10.656570743 + 7.75
x = -10.656570743 + 7.75

Combine like terms: -10.656570743 + 7.75 = -2.906570743
x = -2.906570743

Simplifying
x = -2.906570743

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.406570743, -2.906570743}