2(x+3)(x-1)=150

Solution for 2(x+3)(x-1)=150 equation:

Simplifying
2(x + 3)(x + -1) = 150

Reorder the terms:
2(3 + x)(x + -1) = 150

Reorder the terms:
2(3 + x)(-1 + x) = 150

Multiply (3 + x) * (-1 + x)
2(3(-1 + x) + x(-1 + x)) = 150
2((-1 * 3 + x * 3) + x(-1 + x)) = 150
2((-3 + 3x) + x(-1 + x)) = 150
2(-3 + 3x + (-1 * x + x * x)) = 150
2(-3 + 3x + (-1x + x2)) = 150

Combine like terms: 3x + -1x = 2x
2(-3 + 2x + x2) = 150
(-3 * 2 + 2x * 2 + x2 * 2) = 150
(-6 + 4x + 2x2) = 150

Solving
-6 + 4x + 2x2 = 150

Solving for variable 'x'.

Reorder the terms:
-6 + -150 + 4x + 2x2 = 150 + -150

Combine like terms: -6 + -150 = -156
-156 + 4x + 2x2 = 150 + -150

Combine like terms: 150 + -150 = 0
-156 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-78 + 2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-78 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-78 + 2x + x2 = 0

Solving
-78 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + 2x + 78 + x2 = 0 + 78

Reorder the terms:
-78 + 78 + 2x + x2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + 2x + x2 = 0 + 78
2x + x2 = 0 + 78

Combine like terms: 0 + 78 = 78
2x + x2 = 78

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 = 78 + 1

Reorder the terms:
1 + 2x + x2 = 78 + 1

Combine like terms: 78 + 1 = 79
1 + 2x + x2 = 79

Factor a perfect square on the left side:
(x + 1)(x + 1) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(x + 1) equal to 8.888194417 and -8.888194417.

Subproblem 1
x + 1 = 8.888194417

Simplifying
x + 1 = 8.888194417

Reorder the terms:
1 + x = 8.888194417

Solving
1 + x = 8.888194417

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 = 8.888194417 + -1

Combine like terms: 1 + -1 = 0
0 + x = 8.888194417 + -1
x = 8.888194417 + -1

Combine like terms: 8.888194417 + -1 = 7.888194417
x = 7.888194417

Simplifying
x = 7.888194417

Subproblem 2
x + 1 = -8.888194417

Simplifying
x + 1 = -8.888194417

Reorder the terms:
1 + x = -8.888194417

Solving
1 + x = -8.888194417

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 = -8.888194417 + -1

Combine like terms: 1 + -1 = 0
0 + x = -8.888194417 + -1
x = -8.888194417 + -1

Combine like terms: -8.888194417 + -1 = -9.888194417
x = -9.888194417

Simplifying
x = -9.888194417

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.888194417, -9.888194417}
Solution
x = {7.888194417, -9.888194417}