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

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


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

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

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

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

Combine like terms: 12x + -30x = -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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