5(9x-3)(-5x-13)=0

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Solution for 5(9x-3)(-5x-13)=0 equation: 


Simplifying
5(9x + -3)(-5x + -13) = 0

Reorder the terms:
5(-3 + 9x)(-5x + -13) = 0

Reorder the terms:
5(-3 + 9x)(-13 + -5x) = 0

Multiply (-3 + 9x) * (-13 + -5x)
5(-3(-13 + -5x) + 9x * (-13 + -5x)) = 0
5((-13 * -3 + -5x * -3) + 9x * (-13 + -5x)) = 0
5((39 + 15x) + 9x * (-13 + -5x)) = 0
5(39 + 15x + (-13 * 9x + -5x * 9x)) = 0
5(39 + 15x + (-117x + -45x2)) = 0

Combine like terms: 15x + -117x = -102x
5(39 + -102x + -45x2) = 0
(39 * 5 + -102x * 5 + -45x2 * 5) = 0
(195 + -510x + -225x2) = 0

Solving
195 + -510x + -225x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(13 + -34x + -15x2) = 0

Factor a trinomial.
15((1 + -3x)(13 + 5x)) = 0

Ignore the factor 15.

Subproblem 1
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

Subproblem 2
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
Solution
x = {0.3333333333, -2.6}

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