(x+2)(x+4)=20+10x

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Solution for (x+2)(x+4)=20+10x equation:


Simplifying
(x + 2)(x + 4) = 20 + 10x

Reorder the terms:
(2 + x)(x + 4) = 20 + 10x

Reorder the terms:
(2 + x)(4 + x) = 20 + 10x

Multiply (2 + x) * (4 + x)
(2(4 + x) + x(4 + x)) = 20 + 10x
((4 * 2 + x * 2) + x(4 + x)) = 20 + 10x
((8 + 2x) + x(4 + x)) = 20 + 10x
(8 + 2x + (4 * x + x * x)) = 20 + 10x
(8 + 2x + (4x + x2)) = 20 + 10x

Combine like terms: 2x + 4x = 6x
(8 + 6x + x2) = 20 + 10x

Solving
8 + 6x + x2 = 20 + 10x

Solving for variable 'x'.

Reorder the terms:
8 + -20 + 6x + -10x + x2 = 20 + 10x + -20 + -10x

Combine like terms: 8 + -20 = -12
-12 + 6x + -10x + x2 = 20 + 10x + -20 + -10x

Combine like terms: 6x + -10x = -4x
-12 + -4x + x2 = 20 + 10x + -20 + -10x

Reorder the terms:
-12 + -4x + x2 = 20 + -20 + 10x + -10x

Combine like terms: 20 + -20 = 0
-12 + -4x + x2 = 0 + 10x + -10x
-12 + -4x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-12 + -4x + x2 = 0

Factor a trinomial.
(-2 + -1x)(6 + -1x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-2, 6}

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