(3x+5)(4x+2)=0

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Solution for (3x+5)(4x+2)=0 equation: 


Simplifying
(3x + 5)(4x + 2) = 0

Reorder the terms:
(5 + 3x)(4x + 2) = 0

Reorder the terms:
(5 + 3x)(2 + 4x) = 0

Multiply (5 + 3x) * (2 + 4x)
(5(2 + 4x) + 3x * (2 + 4x)) = 0
((2 * 5 + 4x * 5) + 3x * (2 + 4x)) = 0
((10 + 20x) + 3x * (2 + 4x)) = 0
(10 + 20x + (2 * 3x + 4x * 3x)) = 0
(10 + 20x + (6x + 12x2)) = 0

Combine like terms: 20x + 6x = 26x
(10 + 26x + 12x2) = 0

Solving
10 + 26x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 13x + 6x2) = 0

Factor a trinomial.
2((5 + 3x)(1 + 2x)) = 0

Ignore the factor 2.

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 '(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
Solution
x = {-1.666666667, -0.5}

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