(3x-6)(5x+4)=0

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Solution for (3x-6)(5x+4)=0 equation: 


Simplifying
(3x + -6)(5x + 4) = 0

Reorder the terms:
(-6 + 3x)(5x + 4) = 0

Reorder the terms:
(-6 + 3x)(4 + 5x) = 0

Multiply (-6 + 3x) * (4 + 5x)
(-6(4 + 5x) + 3x * (4 + 5x)) = 0
((4 * -6 + 5x * -6) + 3x * (4 + 5x)) = 0
((-24 + -30x) + 3x * (4 + 5x)) = 0
(-24 + -30x + (4 * 3x + 5x * 3x)) = 0
(-24 + -30x + (12x + 15x2)) = 0

Combine like terms: -30x + 12x = -18x
(-24 + -18x + 15x2) = 0

Solving
-24 + -18x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -6x + 5x2) = 0

Factor a trinomial.
3((-4 + -5x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.8, 2}

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