(x+4)(x+2)=24

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Solution for (x+4)(x+2)=24 equation:


Simplifying
(x + 4)(x + 2) = 24

Reorder the terms:
(4 + x)(x + 2) = 24

Reorder the terms:
(4 + x)(2 + x) = 24

Multiply (4 + x) * (2 + x)
(4(2 + x) + x(2 + x)) = 24
((2 * 4 + x * 4) + x(2 + x)) = 24
((8 + 4x) + x(2 + x)) = 24
(8 + 4x + (2 * x + x * x)) = 24
(8 + 4x + (2x + x2)) = 24

Combine like terms: 4x + 2x = 6x
(8 + 6x + x2) = 24

Solving
8 + 6x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
8 + -24 + 6x + x2 = 24 + -24

Combine like terms: 8 + -24 = -16
-16 + 6x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-16 + 6x + x2 = 0

Factor a trinomial.
(-8 + -1x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-8, 2}

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