(3x+2)(-5x-4)=0

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Solution for (3x+2)(-5x-4)=0 equation: 


Simplifying
(3x + 2)(-5x + -4) = 0

Reorder the terms:
(2 + 3x)(-5x + -4) = 0

Reorder the terms:
(2 + 3x)(-4 + -5x) = 0

Multiply (2 + 3x) * (-4 + -5x)
(2(-4 + -5x) + 3x * (-4 + -5x)) = 0
((-4 * 2 + -5x * 2) + 3x * (-4 + -5x)) = 0
((-8 + -10x) + 3x * (-4 + -5x)) = 0
(-8 + -10x + (-4 * 3x + -5x * 3x)) = 0
(-8 + -10x + (-12x + -15x2)) = 0

Combine like terms: -10x + -12x = -22x
(-8 + -22x + -15x2) = 0

Solving
-8 + -22x + -15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 22x + 15x2) = 0

Factor a trinomial.
-1((4 + 5x)(2 + 3x)) = 0

Ignore the factor -1.

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 + 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
Solution
x = {-0.8, -0.6666666667}

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