(5x-1)(3x+9)=0

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Solution for (5x-1)(3x+9)=0 equation: 


Simplifying
(5x + -1)(3x + 9) = 0

Reorder the terms:
(-1 + 5x)(3x + 9) = 0

Reorder the terms:
(-1 + 5x)(9 + 3x) = 0

Multiply (-1 + 5x) * (9 + 3x)
(-1(9 + 3x) + 5x * (9 + 3x)) = 0
((9 * -1 + 3x * -1) + 5x * (9 + 3x)) = 0
((-9 + -3x) + 5x * (9 + 3x)) = 0
(-9 + -3x + (9 * 5x + 3x * 5x)) = 0
(-9 + -3x + (45x + 15x2)) = 0

Combine like terms: -3x + 45x = 42x
(-9 + 42x + 15x2) = 0

Solving
-9 + 42x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 14x + 5x2) = 0

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

Ignore the factor 3.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {-3, 0.2}

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