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

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


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

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

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

Multiply (13 + 3x) * (-5 + 3x)
(13(-5 + 3x) + 3x * (-5 + 3x)) = 0
((-5 * 13 + 3x * 13) + 3x * (-5 + 3x)) = 0
((-65 + 39x) + 3x * (-5 + 3x)) = 0
(-65 + 39x + (-5 * 3x + 3x * 3x)) = 0
(-65 + 39x + (-15x + 9x2)) = 0

Combine like terms: 39x + -15x = 24x
(-65 + 24x + 9x2) = 0

Solving
-65 + 24x + 9x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-13 + -3x)' equal to zero and attempt to solve:

Simplifying
-13 + -3x = 0

Solving
-13 + -3x = 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 + -3x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -3x = 0 + 13
-3x = 0 + 13

Combine like terms: 0 + 13 = 13
-3x = 13

Divide each side by '-3'.
x = -4.333333333

Simplifying
x = -4.333333333

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 = {-4.333333333, 1.666666667}

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