(3x+4)(-2x-1)=0

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Solution for (3x+4)(-2x-1)=0 equation: 


Simplifying
(3x + 4)(-2x + -1) = 0

Reorder the terms:
(4 + 3x)(-2x + -1) = 0

Reorder the terms:
(4 + 3x)(-1 + -2x) = 0

Multiply (4 + 3x) * (-1 + -2x)
(4(-1 + -2x) + 3x * (-1 + -2x)) = 0
((-1 * 4 + -2x * 4) + 3x * (-1 + -2x)) = 0
((-4 + -8x) + 3x * (-1 + -2x)) = 0
(-4 + -8x + (-1 * 3x + -2x * 3x)) = 0
(-4 + -8x + (-3x + -6x2)) = 0

Combine like terms: -8x + -3x = -11x
(-4 + -11x + -6x2) = 0

Solving
-4 + -11x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 11x + 6x2) = 0

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

Ignore the factor -1.

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

Simplifying
4 + 3x = 0

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

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

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

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

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

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-1.333333333, -0.5}

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