(3x-5)(9x+4)=0

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Solution for (3x-5)(9x+4)=0 equation: 


Simplifying
(3x + -5)(9x + 4) = 0

Reorder the terms:
(-5 + 3x)(9x + 4) = 0

Reorder the terms:
(-5 + 3x)(4 + 9x) = 0

Multiply (-5 + 3x) * (4 + 9x)
(-5(4 + 9x) + 3x * (4 + 9x)) = 0
((4 * -5 + 9x * -5) + 3x * (4 + 9x)) = 0
((-20 + -45x) + 3x * (4 + 9x)) = 0
(-20 + -45x + (4 * 3x + 9x * 3x)) = 0
(-20 + -45x + (12x + 27x2)) = 0

Combine like terms: -45x + 12x = -33x
(-20 + -33x + 27x2) = 0

Solving
-20 + -33x + 27x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -9x)(5 + -3x) = 0


Subproblem 1
Set the factor '(-4 + -9x)' equal to zero and attempt to solve:

Simplifying
-4 + -9x = 0

Solving
-4 + -9x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -9x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -9x = 0 + 4
-9x = 0 + 4

Combine like terms: 0 + 4 = 4
-9x = 4

Divide each side by '-9'.
x = -0.4444444444

Simplifying
x = -0.4444444444

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 = {-0.4444444444, 1.666666667}

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