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

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


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

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

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

Multiply (-3 + -4x) * (2 + 5x)
(-3(2 + 5x) + -4x * (2 + 5x)) = 0
((2 * -3 + 5x * -3) + -4x * (2 + 5x)) = 0
((-6 + -15x) + -4x * (2 + 5x)) = 0
(-6 + -15x + (2 * -4x + 5x * -4x)) = 0
(-6 + -15x + (-8x + -20x2)) = 0

Combine like terms: -15x + -8x = -23x
(-6 + -23x + -20x2) = 0

Solving
-6 + -23x + -20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 23x + 20x2) = 0

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

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 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 + 4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x = 0 + -3
4x = 0 + -3

Combine like terms: 0 + -3 = -3
4x = -3

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75

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 = {-0.75, -0.4}

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