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

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


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

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

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

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

Combine like terms: -3x + -8x = -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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