(2x-6)(x+4)=898

Solution for (2x-6)(x+4)=898 equation:

Simplifying
(2x + -6)(x + 4) = 898

Reorder the terms:
(-6 + 2x)(x + 4) = 898

Reorder the terms:
(-6 + 2x)(4 + x) = 898

Multiply (-6 + 2x) * (4 + x)
(-6(4 + x) + 2x * (4 + x)) = 898
((4 * -6 + x * -6) + 2x * (4 + x)) = 898
((-24 + -6x) + 2x * (4 + x)) = 898
(-24 + -6x + (4 * 2x + x * 2x)) = 898
(-24 + -6x + (8x + 2x2)) = 898

Combine like terms: -6x + 8x = 2x
(-24 + 2x + 2x2) = 898

Solving
-24 + 2x + 2x2 = 898

Solving for variable 'x'.

Reorder the terms:
-24 + -898 + 2x + 2x2 = 898 + -898

Combine like terms: -24 + -898 = -922
-922 + 2x + 2x2 = 898 + -898

Combine like terms: 898 + -898 = 0
-922 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-461 + x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-461 + x + x2)' equal to zero and attempt to solve:

Simplifying
-461 + x + x2 = 0

Solving
-461 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '461' to each side of the equation.
-461 + x + 461 + x2 = 0 + 461

Reorder the terms:
-461 + 461 + x + x2 = 0 + 461

Combine like terms: -461 + 461 = 0
0 + x + x2 = 0 + 461
x + x2 = 0 + 461

Combine like terms: 0 + 461 = 461
x + x2 = 461

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 461 + 0.25

Reorder the terms:
0.25 + x + x2 = 461 + 0.25

Combine like terms: 461 + 0.25 = 461.25
0.25 + x + x2 = 461.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 461.25

Calculate the square root of the right side: 21.476731595

Break this problem into two subproblems by setting 
(x + 0.5) equal to 21.476731595 and -21.476731595.

Subproblem 1
x + 0.5 = 21.476731595

Simplifying
x + 0.5 = 21.476731595

Reorder the terms:
0.5 + x = 21.476731595

Solving
0.5 + x = 21.476731595

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 21.476731595 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 21.476731595 + -0.5
x = 21.476731595 + -0.5

Combine like terms: 21.476731595 + -0.5 = 20.976731595
x = 20.976731595

Simplifying
x = 20.976731595

Subproblem 2
x + 0.5 = -21.476731595

Simplifying
x + 0.5 = -21.476731595

Reorder the terms:
0.5 + x = -21.476731595

Solving
0.5 + x = -21.476731595

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -21.476731595 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -21.476731595 + -0.5
x = -21.476731595 + -0.5

Combine like terms: -21.476731595 + -0.5 = -21.976731595
x = -21.976731595

Simplifying
x = -21.976731595

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.976731595, -21.976731595}
Solution
x = {20.976731595, -21.976731595}