(x+2)(x+6)=x

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Solution for (x+2)(x+6)=x equation:


Simplifying
(x + 2)(x + 6) = x

Reorder the terms:
(2 + x)(x + 6) = x

Reorder the terms:
(2 + x)(6 + x) = x

Multiply (2 + x) * (6 + x)
(2(6 + x) + x(6 + x)) = x
((6 * 2 + x * 2) + x(6 + x)) = x
((12 + 2x) + x(6 + x)) = x
(12 + 2x + (6 * x + x * x)) = x
(12 + 2x + (6x + x2)) = x

Combine like terms: 2x + 6x = 8x
(12 + 8x + x2) = x

Solving
12 + 8x + x2 = x

Solving for variable 'x'.

Reorder the terms:
12 + 8x + -1x + x2 = x + -1x

Combine like terms: 8x + -1x = 7x
12 + 7x + x2 = x + -1x

Combine like terms: x + -1x = 0
12 + 7x + x2 = 0

Factor a trinomial.
(4 + x)(3 + x) = 0

Subproblem 1

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 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 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {-4, -3}

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