(x+2)(x+4)+1=4(x+2+x+4)

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Solution for (x+2)(x+4)+1=4(x+2+x+4) equation: 


Simplifying
(x + 2)(x + 4) + 1 = 4(x + 2 + x + 4)

Reorder the terms:
(2 + x)(x + 4) + 1 = 4(x + 2 + x + 4)

Reorder the terms:
(2 + x)(4 + x) + 1 = 4(x + 2 + x + 4)

Multiply (2 + x) * (4 + x)
(2(4 + x) + x(4 + x)) + 1 = 4(x + 2 + x + 4)
((4 * 2 + x * 2) + x(4 + x)) + 1 = 4(x + 2 + x + 4)
((8 + 2x) + x(4 + x)) + 1 = 4(x + 2 + x + 4)
(8 + 2x + (4 * x + x * x)) + 1 = 4(x + 2 + x + 4)
(8 + 2x + (4x + x2)) + 1 = 4(x + 2 + x + 4)

Combine like terms: 2x + 4x = 6x
(8 + 6x + x2) + 1 = 4(x + 2 + x + 4)

Reorder the terms:
8 + 1 + 6x + x2 = 4(x + 2 + x + 4)

Combine like terms: 8 + 1 = 9
9 + 6x + x2 = 4(x + 2 + x + 4)

Reorder the terms:
9 + 6x + x2 = 4(2 + 4 + x + x)

Combine like terms: 2 + 4 = 6
9 + 6x + x2 = 4(6 + x + x)

Combine like terms: x + x = 2x
9 + 6x + x2 = 4(6 + 2x)
9 + 6x + x2 = (6 * 4 + 2x * 4)
9 + 6x + x2 = (24 + 8x)

Solving
9 + 6x + x2 = 24 + 8x

Solving for variable 'x'.

Reorder the terms:
9 + -24 + 6x + -8x + x2 = 24 + 8x + -24 + -8x

Combine like terms: 9 + -24 = -15
-15 + 6x + -8x + x2 = 24 + 8x + -24 + -8x

Combine like terms: 6x + -8x = -2x
-15 + -2x + x2 = 24 + 8x + -24 + -8x

Reorder the terms:
-15 + -2x + x2 = 24 + -24 + 8x + -8x

Combine like terms: 24 + -24 = 0
-15 + -2x + x2 = 0 + 8x + -8x
-15 + -2x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-15 + -2x + x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3, 5}

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