2(x+3)(x-1)=176

Solution for 2(x+3)(x-1)=176 equation:

Simplifying
2(x + 3)(x + -1) = 176

Reorder the terms:
2(3 + x)(x + -1) = 176

Reorder the terms:
2(3 + x)(-1 + x) = 176

Multiply (3 + x) * (-1 + x)
2(3(-1 + x) + x(-1 + x)) = 176
2((-1 * 3 + x * 3) + x(-1 + x)) = 176
2((-3 + 3x) + x(-1 + x)) = 176
2(-3 + 3x + (-1 * x + x * x)) = 176
2(-3 + 3x + (-1x + x2)) = 176

Combine like terms: 3x + -1x = 2x
2(-3 + 2x + x2) = 176
(-3 * 2 + 2x * 2 + x2 * 2) = 176
(-6 + 4x + 2x2) = 176

Solving
-6 + 4x + 2x2 = 176

Solving for variable 'x'.

Reorder the terms:
-6 + -176 + 4x + 2x2 = 176 + -176

Combine like terms: -6 + -176 = -182
-182 + 4x + 2x2 = 176 + -176

Combine like terms: 176 + -176 = 0
-182 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-91 + 2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-91 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-91 + 2x + x2 = 0

Solving
-91 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '91' to each side of the equation.
-91 + 2x + 91 + x2 = 0 + 91

Reorder the terms:
-91 + 91 + 2x + x2 = 0 + 91

Combine like terms: -91 + 91 = 0
0 + 2x + x2 = 0 + 91
2x + x2 = 0 + 91

Combine like terms: 0 + 91 = 91
2x + x2 = 91

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 = 91 + 1

Reorder the terms:
1 + 2x + x2 = 91 + 1

Combine like terms: 91 + 1 = 92
1 + 2x + x2 = 92

Factor a perfect square on the left side:
(x + 1)(x + 1) = 92

Calculate the square root of the right side: 9.591663047

Break this problem into two subproblems by setting 
(x + 1) equal to 9.591663047 and -9.591663047.

Subproblem 1
x + 1 = 9.591663047

Simplifying
x + 1 = 9.591663047

Reorder the terms:
1 + x = 9.591663047

Solving
1 + x = 9.591663047

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 = 9.591663047 + -1

Combine like terms: 1 + -1 = 0
0 + x = 9.591663047 + -1
x = 9.591663047 + -1

Combine like terms: 9.591663047 + -1 = 8.591663047
x = 8.591663047

Simplifying
x = 8.591663047

Subproblem 2
x + 1 = -9.591663047

Simplifying
x + 1 = -9.591663047

Reorder the terms:
1 + x = -9.591663047

Solving
1 + x = -9.591663047

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 = -9.591663047 + -1

Combine like terms: 1 + -1 = 0
0 + x = -9.591663047 + -1
x = -9.591663047 + -1

Combine like terms: -9.591663047 + -1 = -10.591663047
x = -10.591663047

Simplifying
x = -10.591663047

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.591663047, -10.591663047}
Solution
x = {8.591663047, -10.591663047}