(3x+5)(2x+4)+(4x+2)(3x+5)=x

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Solution for (3x+5)(2x+4)+(4x+2)(3x+5)=x equation:


Simplifying
(3x + 5)(2x + 4) + (4x + 2)(3x + 5) = x

Reorder the terms:
(5 + 3x)(2x + 4) + (4x + 2)(3x + 5) = x

Reorder the terms:
(5 + 3x)(4 + 2x) + (4x + 2)(3x + 5) = x

Multiply (5 + 3x) * (4 + 2x)
(5(4 + 2x) + 3x * (4 + 2x)) + (4x + 2)(3x + 5) = x
((4 * 5 + 2x * 5) + 3x * (4 + 2x)) + (4x + 2)(3x + 5) = x
((20 + 10x) + 3x * (4 + 2x)) + (4x + 2)(3x + 5) = x
(20 + 10x + (4 * 3x + 2x * 3x)) + (4x + 2)(3x + 5) = x
(20 + 10x + (12x + 6x2)) + (4x + 2)(3x + 5) = x

Combine like terms: 10x + 12x = 22x
(20 + 22x + 6x2) + (4x + 2)(3x + 5) = x

Reorder the terms:
20 + 22x + 6x2 + (2 + 4x)(3x + 5) = x

Reorder the terms:
20 + 22x + 6x2 + (2 + 4x)(5 + 3x) = x

Multiply (2 + 4x) * (5 + 3x)
20 + 22x + 6x2 + (2(5 + 3x) + 4x * (5 + 3x)) = x
20 + 22x + 6x2 + ((5 * 2 + 3x * 2) + 4x * (5 + 3x)) = x
20 + 22x + 6x2 + ((10 + 6x) + 4x * (5 + 3x)) = x
20 + 22x + 6x2 + (10 + 6x + (5 * 4x + 3x * 4x)) = x
20 + 22x + 6x2 + (10 + 6x + (20x + 12x2)) = x

Combine like terms: 6x + 20x = 26x
20 + 22x + 6x2 + (10 + 26x + 12x2) = x

Reorder the terms:
20 + 10 + 22x + 26x + 6x2 + 12x2 = x

Combine like terms: 20 + 10 = 30
30 + 22x + 26x + 6x2 + 12x2 = x

Combine like terms: 22x + 26x = 48x
30 + 48x + 6x2 + 12x2 = x

Combine like terms: 6x2 + 12x2 = 18x2
30 + 48x + 18x2 = x

Solving
30 + 48x + 18x2 = x

Solving for variable 'x'.

Reorder the terms:
30 + 48x + -1x + 18x2 = x + -1x

Combine like terms: 48x + -1x = 47x
30 + 47x + 18x2 = x + -1x

Combine like terms: x + -1x = 0
30 + 47x + 18x2 = 0

Factor a trinomial.
(3 + 2x)(10 + 9x) = 0


Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(10 + 9x)' equal to zero and attempt to solve:

Simplifying
10 + 9x = 0

Solving
10 + 9x = 0

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

Add '-10' to each side of the equation.
10 + -10 + 9x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 9x = 0 + -10
9x = 0 + -10

Combine like terms: 0 + -10 = -10
9x = -10

Divide each side by '9'.
x = -1.111111111

Simplifying
x = -1.111111111
Solution
x = {-1.5, -1.111111111}

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