2(x+7)(x-3)=114

Solution for 2(x+7)(x-3)=114 equation:

Simplifying
2(x + 7)(x + -3) = 114

Reorder the terms:
2(7 + x)(x + -3) = 114

Reorder the terms:
2(7 + x)(-3 + x) = 114

Multiply (7 + x) * (-3 + x)
2(7(-3 + x) + x(-3 + x)) = 114
2((-3 * 7 + x * 7) + x(-3 + x)) = 114
2((-21 + 7x) + x(-3 + x)) = 114
2(-21 + 7x + (-3 * x + x * x)) = 114
2(-21 + 7x + (-3x + x2)) = 114

Combine like terms: 7x + -3x = 4x
2(-21 + 4x + x2) = 114
(-21 * 2 + 4x * 2 + x2 * 2) = 114
(-42 + 8x + 2x2) = 114

Solving
-42 + 8x + 2x2 = 114

Solving for variable 'x'.

Reorder the terms:
-42 + -114 + 8x + 2x2 = 114 + -114

Combine like terms: -42 + -114 = -156
-156 + 8x + 2x2 = 114 + -114

Combine like terms: 114 + -114 = 0
-156 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-78 + 4x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-78 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-78 + 4x + x2 = 0

Solving
-78 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + 4x + 78 + x2 = 0 + 78

Reorder the terms:
-78 + 78 + 4x + x2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + 4x + x2 = 0 + 78
4x + x2 = 0 + 78

Combine like terms: 0 + 78 = 78
4x + x2 = 78

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 78 + 4

Reorder the terms:
4 + 4x + x2 = 78 + 4

Combine like terms: 78 + 4 = 82
4 + 4x + x2 = 82

Factor a perfect square on the left side:
(x + 2)(x + 2) = 82

Calculate the square root of the right side: 9.055385138

Break this problem into two subproblems by setting 
(x + 2) equal to 9.055385138 and -9.055385138.

Subproblem 1
x + 2 = 9.055385138

Simplifying
x + 2 = 9.055385138

Reorder the terms:
2 + x = 9.055385138

Solving
2 + x = 9.055385138

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 9.055385138 + -2

Combine like terms: 2 + -2 = 0
0 + x = 9.055385138 + -2
x = 9.055385138 + -2

Combine like terms: 9.055385138 + -2 = 7.055385138
x = 7.055385138

Simplifying
x = 7.055385138

Subproblem 2
x + 2 = -9.055385138

Simplifying
x + 2 = -9.055385138

Reorder the terms:
2 + x = -9.055385138

Solving
2 + x = -9.055385138

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -9.055385138 + -2

Combine like terms: 2 + -2 = 0
0 + x = -9.055385138 + -2
x = -9.055385138 + -2

Combine like terms: -9.055385138 + -2 = -11.055385138
x = -11.055385138

Simplifying
x = -11.055385138

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.055385138, -11.055385138}
Solution
x = {7.055385138, -11.055385138}