(3x+5)(2x+13)=0

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Solution for (3x+5)(2x+13)=0 equation: 


Simplifying
(3x + 5)(2x + 13) = 0

Reorder the terms:
(5 + 3x)(2x + 13) = 0

Reorder the terms:
(5 + 3x)(13 + 2x) = 0

Multiply (5 + 3x) * (13 + 2x)
(5(13 + 2x) + 3x * (13 + 2x)) = 0
((13 * 5 + 2x * 5) + 3x * (13 + 2x)) = 0
((65 + 10x) + 3x * (13 + 2x)) = 0
(65 + 10x + (13 * 3x + 2x * 3x)) = 0
(65 + 10x + (39x + 6x2)) = 0

Combine like terms: 10x + 39x = 49x
(65 + 49x + 6x2) = 0

Solving
65 + 49x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + 2x)(5 + 3x) = 0


Subproblem 1
Set the factor '(13 + 2x)' equal to zero and attempt to solve:

Simplifying
13 + 2x = 0

Solving
13 + 2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 2x = 0 + -13
2x = 0 + -13

Combine like terms: 0 + -13 = -13
2x = -13

Divide each side by '2'.
x = -6.5

Simplifying
x = -6.5

Subproblem 2
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
Solution
x = {-6.5, -1.666666667}

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