(5x+13)(3x+7)=0

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Solution for (5x+13)(3x+7)=0 equation: 


Simplifying
(5x + 13)(3x + 7) = 0

Reorder the terms:
(13 + 5x)(3x + 7) = 0

Reorder the terms:
(13 + 5x)(7 + 3x) = 0

Multiply (13 + 5x) * (7 + 3x)
(13(7 + 3x) + 5x * (7 + 3x)) = 0
((7 * 13 + 3x * 13) + 5x * (7 + 3x)) = 0
((91 + 39x) + 5x * (7 + 3x)) = 0
(91 + 39x + (7 * 5x + 3x * 5x)) = 0
(91 + 39x + (35x + 15x2)) = 0

Combine like terms: 39x + 35x = 74x
(91 + 74x + 15x2) = 0

Solving
91 + 74x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + 5x)(7 + 3x) = 0


Subproblem 1
Set the factor '(13 + 5x)' equal to zero and attempt to solve:

Simplifying
13 + 5x = 0

Solving
13 + 5x = 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 + 5x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 5x = 0 + -13
5x = 0 + -13

Combine like terms: 0 + -13 = -13
5x = -13

Divide each side by '5'.
x = -2.6

Simplifying
x = -2.6

Subproblem 2
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333
Solution
x = {-2.6, -2.333333333}

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