(x+2)(x+4)-20=0

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Solution for (x+2)(x+4)-20=0 equation:


Simplifying
(x + 2)(x + 4) + -20 = 0

Reorder the terms:
(2 + x)(x + 4) + -20 = 0

Reorder the terms:
(2 + x)(4 + x) + -20 = 0

Multiply (2 + x) * (4 + x)
(2(4 + x) + x(4 + x)) + -20 = 0
((4 * 2 + x * 2) + x(4 + x)) + -20 = 0
((8 + 2x) + x(4 + x)) + -20 = 0
(8 + 2x + (4 * x + x * x)) + -20 = 0
(8 + 2x + (4x + x2)) + -20 = 0

Combine like terms: 2x + 4x = 6x
(8 + 6x + x2) + -20 = 0

Reorder the terms:
8 + -20 + 6x + x2 = 0

Combine like terms: 8 + -20 = -12
-12 + 6x + x2 = 0

Solving
-12 + 6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 6x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 6x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 6x + x2 = 0 + 12
6x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
6x + x2 = 12

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 12 + 9

Reorder the terms:
9 + 6x + x2 = 12 + 9

Combine like terms: 12 + 9 = 21
9 + 6x + x2 = 21

Factor a perfect square on the left side:
(x + 3)(x + 3) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + 3) equal to 4.582575695 and -4.582575695.

Subproblem 1

x + 3 = 4.582575695 Simplifying x + 3 = 4.582575695 Reorder the terms: 3 + x = 4.582575695 Solving 3 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.582575695 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.582575695 + -3 x = 4.582575695 + -3 Combine like terms: 4.582575695 + -3 = 1.582575695 x = 1.582575695 Simplifying x = 1.582575695

Subproblem 2

x + 3 = -4.582575695 Simplifying x + 3 = -4.582575695 Reorder the terms: 3 + x = -4.582575695 Solving 3 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.582575695 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.582575695 + -3 x = -4.582575695 + -3 Combine like terms: -4.582575695 + -3 = -7.582575695 x = -7.582575695 Simplifying x = -7.582575695

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.582575695, -7.582575695}

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