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

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


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

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

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

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

Combine like terms: -8x + 3x = -5x
(-12 + -5x + 2x2) = 0

Solving
-12 + -5x + 2x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-1.5, 4}

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