(-5x-2)(3x+2)=0

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Solution for (-5x-2)(3x+2)=0 equation: 


Simplifying
(-5x + -2)(3x + 2) = 0

Reorder the terms:
(-2 + -5x)(3x + 2) = 0

Reorder the terms:
(-2 + -5x)(2 + 3x) = 0

Multiply (-2 + -5x) * (2 + 3x)
(-2(2 + 3x) + -5x * (2 + 3x)) = 0
((2 * -2 + 3x * -2) + -5x * (2 + 3x)) = 0
((-4 + -6x) + -5x * (2 + 3x)) = 0
(-4 + -6x + (2 * -5x + 3x * -5x)) = 0
(-4 + -6x + (-10x + -15x2)) = 0

Combine like terms: -6x + -10x = -16x
(-4 + -16x + -15x2) = 0

Solving
-4 + -16x + -15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 16x + 15x2) = 0

Factor a trinomial.
-1((2 + 3x)(2 + 5x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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

Simplifying
2 + 5x = 0

Solving
2 + 5x = 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 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2

Combine like terms: 0 + -2 = -2
5x = -2

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4
Solution
x = {-0.6666666667, -0.4}

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