(3x+1)(4x+2)=(3x+1)(x-2)

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Solution for (3x+1)(4x+2)=(3x+1)(x-2) equation: 


Simplifying
(3x + 1)(4x + 2) = (3x + 1)(x + -2)

Reorder the terms:
(1 + 3x)(4x + 2) = (3x + 1)(x + -2)

Reorder the terms:
(1 + 3x)(2 + 4x) = (3x + 1)(x + -2)

Multiply (1 + 3x) * (2 + 4x)
(1(2 + 4x) + 3x * (2 + 4x)) = (3x + 1)(x + -2)
((2 * 1 + 4x * 1) + 3x * (2 + 4x)) = (3x + 1)(x + -2)
((2 + 4x) + 3x * (2 + 4x)) = (3x + 1)(x + -2)
(2 + 4x + (2 * 3x + 4x * 3x)) = (3x + 1)(x + -2)
(2 + 4x + (6x + 12x2)) = (3x + 1)(x + -2)

Combine like terms: 4x + 6x = 10x
(2 + 10x + 12x2) = (3x + 1)(x + -2)

Reorder the terms:
2 + 10x + 12x2 = (1 + 3x)(x + -2)

Reorder the terms:
2 + 10x + 12x2 = (1 + 3x)(-2 + x)

Multiply (1 + 3x) * (-2 + x)
2 + 10x + 12x2 = (1(-2 + x) + 3x * (-2 + x))
2 + 10x + 12x2 = ((-2 * 1 + x * 1) + 3x * (-2 + x))
2 + 10x + 12x2 = ((-2 + 1x) + 3x * (-2 + x))
2 + 10x + 12x2 = (-2 + 1x + (-2 * 3x + x * 3x))
2 + 10x + 12x2 = (-2 + 1x + (-6x + 3x2))

Combine like terms: 1x + -6x = -5x
2 + 10x + 12x2 = (-2 + -5x + 3x2)

Solving
2 + 10x + 12x2 = -2 + -5x + 3x2

Solving for variable 'x'.

Reorder the terms:
2 + 2 + 10x + 5x + 12x2 + -3x2 = -2 + -5x + 3x2 + 2 + 5x + -3x2

Combine like terms: 2 + 2 = 4
4 + 10x + 5x + 12x2 + -3x2 = -2 + -5x + 3x2 + 2 + 5x + -3x2

Combine like terms: 10x + 5x = 15x
4 + 15x + 12x2 + -3x2 = -2 + -5x + 3x2 + 2 + 5x + -3x2

Combine like terms: 12x2 + -3x2 = 9x2
4 + 15x + 9x2 = -2 + -5x + 3x2 + 2 + 5x + -3x2

Reorder the terms:
4 + 15x + 9x2 = -2 + 2 + -5x + 5x + 3x2 + -3x2

Combine like terms: -2 + 2 = 0
4 + 15x + 9x2 = 0 + -5x + 5x + 3x2 + -3x2
4 + 15x + 9x2 = -5x + 5x + 3x2 + -3x2

Combine like terms: -5x + 5x = 0
4 + 15x + 9x2 = 0 + 3x2 + -3x2
4 + 15x + 9x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
4 + 15x + 9x2 = 0

Factor a trinomial.
(4 + 3x)(1 + 3x) = 0


Subproblem 1
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333

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

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3x = 0 + -1

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

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

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-1.333333333, -0.3333333333}

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