(x-4)(x+2)=12

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Solution for (x-4)(x+2)=12 equation:


Simplifying
(x + -4)(x + 2) = 12

Reorder the terms:
(-4 + x)(x + 2) = 12

Reorder the terms:
(-4 + x)(2 + x) = 12

Multiply (-4 + x) * (2 + x)
(-4(2 + x) + x(2 + x)) = 12
((2 * -4 + x * -4) + x(2 + x)) = 12
((-8 + -4x) + x(2 + x)) = 12
(-8 + -4x + (2 * x + x * x)) = 12
(-8 + -4x + (2x + x2)) = 12

Combine like terms: -4x + 2x = -2x
(-8 + -2x + x2) = 12

Solving
-8 + -2x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
-8 + -12 + -2x + x2 = 12 + -12

Combine like terms: -8 + -12 = -20
-20 + -2x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-20 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -2x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -2x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -2x + x2 = 0 + 20
-2x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-2x + x2 = 20

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 = 20 + 1

Reorder the terms:
1 + -2x + x2 = 20 + 1

Combine like terms: 20 + 1 = 21
1 + -2x + x2 = 21

Factor a perfect square on the left side:
(x + -1)(x + -1) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + -1) equal to 4.582575695 and -4.582575695.

Subproblem 1

x + -1 = 4.582575695 Simplifying x + -1 = 4.582575695 Reorder the terms: -1 + x = 4.582575695 Solving -1 + x = 4.582575695 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 = 4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.582575695 + 1 x = 4.582575695 + 1 Combine like terms: 4.582575695 + 1 = 5.582575695 x = 5.582575695 Simplifying x = 5.582575695

Subproblem 2

x + -1 = -4.582575695 Simplifying x + -1 = -4.582575695 Reorder the terms: -1 + x = -4.582575695 Solving -1 + x = -4.582575695 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 = -4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.582575695 + 1 x = -4.582575695 + 1 Combine like terms: -4.582575695 + 1 = -3.582575695 x = -3.582575695 Simplifying x = -3.582575695

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.582575695, -3.582575695}

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