2(x+7)(x-3)=144

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Solution for 2(x+7)(x-3)=144 equation: 


Simplifying
2(x + 7)(x + -3) = 144

Reorder the terms:
2(7 + x)(x + -3) = 144

Reorder the terms:
2(7 + x)(-3 + x) = 144

Multiply (7 + x) * (-3 + x)
2(7(-3 + x) + x(-3 + x)) = 144
2((-3 * 7 + x * 7) + x(-3 + x)) = 144
2((-21 + 7x) + x(-3 + x)) = 144
2(-21 + 7x + (-3 * x + x * x)) = 144
2(-21 + 7x + (-3x + x2)) = 144

Combine like terms: 7x + -3x = 4x
2(-21 + 4x + x2) = 144
(-21 * 2 + 4x * 2 + x2 * 2) = 144
(-42 + 8x + 2x2) = 144

Solving
-42 + 8x + 2x2 = 144

Solving for variable 'x'.

Reorder the terms:
-42 + -144 + 8x + 2x2 = 144 + -144

Combine like terms: -42 + -144 = -186
-186 + 8x + 2x2 = 144 + -144

Combine like terms: 144 + -144 = 0
-186 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-93 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-93 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-93 + 4x + x2 = 0

Solving
-93 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '93' to each side of the equation.
-93 + 4x + 93 + x2 = 0 + 93

Reorder the terms:
-93 + 93 + 4x + x2 = 0 + 93

Combine like terms: -93 + 93 = 0
0 + 4x + x2 = 0 + 93
4x + x2 = 0 + 93

Combine like terms: 0 + 93 = 93
4x + x2 = 93

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 = 93 + 4

Reorder the terms:
4 + 4x + x2 = 93 + 4

Combine like terms: 93 + 4 = 97
4 + 4x + x2 = 97

Factor a perfect square on the left side:
(x + 2)(x + 2) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + 2) equal to 9.848857802 and -9.848857802.


Subproblem 1
x + 2 = 9.848857802

Simplifying
x + 2 = 9.848857802

Reorder the terms:
2 + x = 9.848857802

Solving
2 + x = 9.848857802

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 = 9.848857802 + -2

Combine like terms: 2 + -2 = 0
0 + x = 9.848857802 + -2
x = 9.848857802 + -2

Combine like terms: 9.848857802 + -2 = 7.848857802
x = 7.848857802

Simplifying
x = 7.848857802


Subproblem 2
x + 2 = -9.848857802

Simplifying
x + 2 = -9.848857802

Reorder the terms:
2 + x = -9.848857802

Solving
2 + x = -9.848857802

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 = -9.848857802 + -2

Combine like terms: 2 + -2 = 0
0 + x = -9.848857802 + -2
x = -9.848857802 + -2

Combine like terms: -9.848857802 + -2 = -11.848857802
x = -11.848857802

Simplifying
x = -11.848857802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.848857802, -11.848857802}
Solution
x = {7.848857802, -11.848857802}

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