(3x+5)(4x+2)=(3x+2)(x+4)-9x-8

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Solution for (3x+5)(4x+2)=(3x+2)(x+4)-9x-8 equation: 


Simplifying
(3x + 5)(4x + 2) = (3x + 2)(x + 4) + -9x + -8

Reorder the terms:
(5 + 3x)(4x + 2) = (3x + 2)(x + 4) + -9x + -8

Reorder the terms:
(5 + 3x)(2 + 4x) = (3x + 2)(x + 4) + -9x + -8

Multiply (5 + 3x) * (2 + 4x)
(5(2 + 4x) + 3x * (2 + 4x)) = (3x + 2)(x + 4) + -9x + -8
((2 * 5 + 4x * 5) + 3x * (2 + 4x)) = (3x + 2)(x + 4) + -9x + -8
((10 + 20x) + 3x * (2 + 4x)) = (3x + 2)(x + 4) + -9x + -8
(10 + 20x + (2 * 3x + 4x * 3x)) = (3x + 2)(x + 4) + -9x + -8
(10 + 20x + (6x + 12x2)) = (3x + 2)(x + 4) + -9x + -8

Combine like terms: 20x + 6x = 26x
(10 + 26x + 12x2) = (3x + 2)(x + 4) + -9x + -8

Reorder the terms:
10 + 26x + 12x2 = (2 + 3x)(x + 4) + -9x + -8

Reorder the terms:
10 + 26x + 12x2 = (2 + 3x)(4 + x) + -9x + -8

Multiply (2 + 3x) * (4 + x)
10 + 26x + 12x2 = (2(4 + x) + 3x * (4 + x)) + -9x + -8
10 + 26x + 12x2 = ((4 * 2 + x * 2) + 3x * (4 + x)) + -9x + -8
10 + 26x + 12x2 = ((8 + 2x) + 3x * (4 + x)) + -9x + -8
10 + 26x + 12x2 = (8 + 2x + (4 * 3x + x * 3x)) + -9x + -8
10 + 26x + 12x2 = (8 + 2x + (12x + 3x2)) + -9x + -8

Combine like terms: 2x + 12x = 14x
10 + 26x + 12x2 = (8 + 14x + 3x2) + -9x + -8

Reorder the terms:
10 + 26x + 12x2 = 8 + -8 + 14x + -9x + 3x2

Combine like terms: 8 + -8 = 0
10 + 26x + 12x2 = 0 + 14x + -9x + 3x2
10 + 26x + 12x2 = 14x + -9x + 3x2

Combine like terms: 14x + -9x = 5x
10 + 26x + 12x2 = 5x + 3x2

Solving
10 + 26x + 12x2 = 5x + 3x2

Solving for variable 'x'.

Reorder the terms:
10 + 26x + -5x + 12x2 + -3x2 = 5x + 3x2 + -5x + -3x2

Combine like terms: 26x + -5x = 21x
10 + 21x + 12x2 + -3x2 = 5x + 3x2 + -5x + -3x2

Combine like terms: 12x2 + -3x2 = 9x2
10 + 21x + 9x2 = 5x + 3x2 + -5x + -3x2

Reorder the terms:
10 + 21x + 9x2 = 5x + -5x + 3x2 + -3x2

Combine like terms: 5x + -5x = 0
10 + 21x + 9x2 = 0 + 3x2 + -3x2
10 + 21x + 9x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
10 + 21x + 9x2 = 0

Factor a trinomial.
(5 + 3x)(2 + 3x) = 0


Subproblem 1
Set the factor '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 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 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667

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

Simplifying
2 + 3x = 0

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

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

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

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-1.666666667, -0.6666666667}

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