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

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


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

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

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

Multiply (-9 + 3x) * (4 + 5x)
(-9(4 + 5x) + 3x * (4 + 5x)) = 0
((4 * -9 + 5x * -9) + 3x * (4 + 5x)) = 0
((-36 + -45x) + 3x * (4 + 5x)) = 0
(-36 + -45x + (4 * 3x + 5x * 3x)) = 0
(-36 + -45x + (12x + 15x2)) = 0

Combine like terms: -45x + 12x = -33x
(-36 + -33x + 15x2) = 0

Solving
-36 + -33x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -11x + 5x2) = 0

Factor a trinomial.
3((-4 + -5x)(3 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -5x)' equal to zero and attempt to solve:

Simplifying
-4 + -5x = 0

Solving
-4 + -5x = 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 + -5x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5x = 0 + 4
-5x = 0 + 4

Combine like terms: 0 + 4 = 4
-5x = 4

Divide each side by '-5'.
x = -0.8

Simplifying
x = -0.8

Subproblem 2
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
Solution
x = {-0.8, 3}

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