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

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


Simplifying
(3x + 1)(4x + 2) = 0

Reorder the terms:
(1 + 3x)(4x + 2) = 0

Reorder the terms:
(1 + 3x)(2 + 4x) = 0

Multiply (1 + 3x) * (2 + 4x)
(1(2 + 4x) + 3x * (2 + 4x)) = 0
((2 * 1 + 4x * 1) + 3x * (2 + 4x)) = 0
((2 + 4x) + 3x * (2 + 4x)) = 0
(2 + 4x + (2 * 3x + 4x * 3x)) = 0
(2 + 4x + (6x + 12x2)) = 0

Combine like terms: 4x + 6x = 10x
(2 + 10x + 12x2) = 0

Solving
2 + 10x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 5x + 6x2) = 0

Factor a trinomial.
2((1 + 2x)(1 + 3x)) = 0

Ignore the factor 2.

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5

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 = {-0.5, -0.3333333333}

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