(x-3)(x*2-7x+8)=(x-5)(x*2-9x-16)

Solution for (x-3)(x*2-7x+8)=(x-5)(x*2-9x-16) equation:

Simplifying
(x + -3)(x * 2 + -7x + 8) = (x + -5)(x * 2 + -9x + -16)

Reorder the terms:
(-3 + x)(x * 2 + -7x + 8) = (x + -5)(x * 2 + -9x + -16)

Reorder the terms for easier multiplication:
(-3 + x)(2x + -7x + 8) = (x + -5)(x * 2 + -9x + -16)

Reorder the terms:
(-3 + x)(8 + 2x + -7x) = (x + -5)(x * 2 + -9x + -16)

Combine like terms: 2x + -7x = -5x
(-3 + x)(8 + -5x) = (x + -5)(x * 2 + -9x + -16)

Multiply (-3 + x) * (8 + -5x)
(-3(8 + -5x) + x(8 + -5x)) = (x + -5)(x * 2 + -9x + -16)
((8 * -3 + -5x * -3) + x(8 + -5x)) = (x + -5)(x * 2 + -9x + -16)
((-24 + 15x) + x(8 + -5x)) = (x + -5)(x * 2 + -9x + -16)
(-24 + 15x + (8 * x + -5x * x)) = (x + -5)(x * 2 + -9x + -16)
(-24 + 15x + (8x + -5x2)) = (x + -5)(x * 2 + -9x + -16)

Combine like terms: 15x + 8x = 23x
(-24 + 23x + -5x2) = (x + -5)(x * 2 + -9x + -16)

Reorder the terms:
-24 + 23x + -5x2 = (-5 + x)(x * 2 + -9x + -16)

Reorder the terms for easier multiplication:
-24 + 23x + -5x2 = (-5 + x)(2x + -9x + -16)

Reorder the terms:
-24 + 23x + -5x2 = (-5 + x)(-16 + 2x + -9x)

Combine like terms: 2x + -9x = -7x
-24 + 23x + -5x2 = (-5 + x)(-16 + -7x)

Multiply (-5 + x) * (-16 + -7x)
-24 + 23x + -5x2 = (-5(-16 + -7x) + x(-16 + -7x))
-24 + 23x + -5x2 = ((-16 * -5 + -7x * -5) + x(-16 + -7x))
-24 + 23x + -5x2 = ((80 + 35x) + x(-16 + -7x))
-24 + 23x + -5x2 = (80 + 35x + (-16 * x + -7x * x))
-24 + 23x + -5x2 = (80 + 35x + (-16x + -7x2))

Combine like terms: 35x + -16x = 19x
-24 + 23x + -5x2 = (80 + 19x + -7x2)

Solving
-24 + 23x + -5x2 = 80 + 19x + -7x2

Solving for variable 'x'.

Reorder the terms:
-24 + -80 + 23x + -19x + -5x2 + 7x2 = 80 + 19x + -7x2 + -80 + -19x + 7x2

Combine like terms: -24 + -80 = -104
-104 + 23x + -19x + -5x2 + 7x2 = 80 + 19x + -7x2 + -80 + -19x + 7x2

Combine like terms: 23x + -19x = 4x
-104 + 4x + -5x2 + 7x2 = 80 + 19x + -7x2 + -80 + -19x + 7x2

Combine like terms: -5x2 + 7x2 = 2x2
-104 + 4x + 2x2 = 80 + 19x + -7x2 + -80 + -19x + 7x2

Reorder the terms:
-104 + 4x + 2x2 = 80 + -80 + 19x + -19x + -7x2 + 7x2

Combine like terms: 80 + -80 = 0
-104 + 4x + 2x2 = 0 + 19x + -19x + -7x2 + 7x2
-104 + 4x + 2x2 = 19x + -19x + -7x2 + 7x2

Combine like terms: 19x + -19x = 0
-104 + 4x + 2x2 = 0 + -7x2 + 7x2
-104 + 4x + 2x2 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
-104 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-52 + 2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-52 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-52 + 2x + x2 = 0

Solving
-52 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + 2x + 52 + x2 = 0 + 52

Reorder the terms:
-52 + 52 + 2x + x2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + 2x + x2 = 0 + 52
2x + x2 = 0 + 52

Combine like terms: 0 + 52 = 52
2x + x2 = 52

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 = 52 + 1

Reorder the terms:
1 + 2x + x2 = 52 + 1

Combine like terms: 52 + 1 = 53
1 + 2x + x2 = 53

Factor a perfect square on the left side:
(x + 1)(x + 1) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(x + 1) equal to 7.280109889 and -7.280109889.

Subproblem 1
x + 1 = 7.280109889

Simplifying
x + 1 = 7.280109889

Reorder the terms:
1 + x = 7.280109889

Solving
1 + x = 7.280109889

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 = 7.280109889 + -1

Combine like terms: 1 + -1 = 0
0 + x = 7.280109889 + -1
x = 7.280109889 + -1

Combine like terms: 7.280109889 + -1 = 6.280109889
x = 6.280109889

Simplifying
x = 6.280109889

Subproblem 2
x + 1 = -7.280109889

Simplifying
x + 1 = -7.280109889

Reorder the terms:
1 + x = -7.280109889

Solving
1 + x = -7.280109889

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 = -7.280109889 + -1

Combine like terms: 1 + -1 = 0
0 + x = -7.280109889 + -1
x = -7.280109889 + -1

Combine like terms: -7.280109889 + -1 = -8.280109889
x = -8.280109889

Simplifying
x = -8.280109889

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.280109889, -8.280109889}
Solution
x = {6.280109889, -8.280109889}