2(x+4)(x-3)=300

Solution for 2(x+4)(x-3)=300 equation:

Simplifying
2(x + 4)(x + -3) = 300

Reorder the terms:
2(4 + x)(x + -3) = 300

Reorder the terms:
2(4 + x)(-3 + x) = 300

Multiply (4 + x) * (-3 + x)
2(4(-3 + x) + x(-3 + x)) = 300
2((-3 * 4 + x * 4) + x(-3 + x)) = 300
2((-12 + 4x) + x(-3 + x)) = 300
2(-12 + 4x + (-3 * x + x * x)) = 300
2(-12 + 4x + (-3x + x2)) = 300

Combine like terms: 4x + -3x = 1x
2(-12 + 1x + x2) = 300
(-12 * 2 + 1x * 2 + x2 * 2) = 300
(-24 + 2x + 2x2) = 300

Solving
-24 + 2x + 2x2 = 300

Solving for variable 'x'.

Reorder the terms:
-24 + -300 + 2x + 2x2 = 300 + -300

Combine like terms: -24 + -300 = -324
-324 + 2x + 2x2 = 300 + -300

Combine like terms: 300 + -300 = 0
-324 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-162 + x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-162 + x + x2)' equal to zero and attempt to solve:

Simplifying
-162 + x + x2 = 0

Solving
-162 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '162' to each side of the equation.
-162 + x + 162 + x2 = 0 + 162

Reorder the terms:
-162 + 162 + x + x2 = 0 + 162

Combine like terms: -162 + 162 = 0
0 + x + x2 = 0 + 162
x + x2 = 0 + 162

Combine like terms: 0 + 162 = 162
x + x2 = 162

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 = 162 + 0.25

Reorder the terms:
0.25 + x + x2 = 162 + 0.25

Combine like terms: 162 + 0.25 = 162.25
0.25 + x + x2 = 162.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 162.25

Calculate the square root of the right side: 12.737739203

Break this problem into two subproblems by setting 
(x + 0.5) equal to 12.737739203 and -12.737739203.

Subproblem 1
x + 0.5 = 12.737739203

Simplifying
x + 0.5 = 12.737739203

Reorder the terms:
0.5 + x = 12.737739203

Solving
0.5 + x = 12.737739203

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 = 12.737739203 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 12.737739203 + -0.5
x = 12.737739203 + -0.5

Combine like terms: 12.737739203 + -0.5 = 12.237739203
x = 12.237739203

Simplifying
x = 12.237739203

Subproblem 2
x + 0.5 = -12.737739203

Simplifying
x + 0.5 = -12.737739203

Reorder the terms:
0.5 + x = -12.737739203

Solving
0.5 + x = -12.737739203

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 = -12.737739203 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -12.737739203 + -0.5
x = -12.737739203 + -0.5

Combine like terms: -12.737739203 + -0.5 = -13.237739203
x = -13.237739203

Simplifying
x = -13.237739203

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.237739203, -13.237739203}
Solution
x = {12.237739203, -13.237739203}