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

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


Simplifying
(3x + -2) * x(x + 3) = (2x + 1) * x(x + 2)

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

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

Reorder the terms for easier multiplication:
x(-2 + 3x)(3 + x) = (2x + 1) * x(x + 2)

Multiply (-2 + 3x) * (3 + x)
x(-2(3 + x) + 3x * (3 + x)) = (2x + 1) * x(x + 2)
x((3 * -2 + x * -2) + 3x * (3 + x)) = (2x + 1) * x(x + 2)
x((-6 + -2x) + 3x * (3 + x)) = (2x + 1) * x(x + 2)
x(-6 + -2x + (3 * 3x + x * 3x)) = (2x + 1) * x(x + 2)
x(-6 + -2x + (9x + 3x2)) = (2x + 1) * x(x + 2)

Combine like terms: -2x + 9x = 7x
x(-6 + 7x + 3x2) = (2x + 1) * x(x + 2)
(-6 * x + 7x * x + 3x2 * x) = (2x + 1) * x(x + 2)
(-6x + 7x2 + 3x3) = (2x + 1) * x(x + 2)

Reorder the terms:
-6x + 7x2 + 3x3 = (1 + 2x) * x(x + 2)

Reorder the terms:
-6x + 7x2 + 3x3 = (1 + 2x) * x(2 + x)

Reorder the terms for easier multiplication:
-6x + 7x2 + 3x3 = x(1 + 2x)(2 + x)

Multiply (1 + 2x) * (2 + x)
-6x + 7x2 + 3x3 = x(1(2 + x) + 2x * (2 + x))
-6x + 7x2 + 3x3 = x((2 * 1 + x * 1) + 2x * (2 + x))
-6x + 7x2 + 3x3 = x((2 + 1x) + 2x * (2 + x))
-6x + 7x2 + 3x3 = x(2 + 1x + (2 * 2x + x * 2x))
-6x + 7x2 + 3x3 = x(2 + 1x + (4x + 2x2))

Combine like terms: 1x + 4x = 5x
-6x + 7x2 + 3x3 = x(2 + 5x + 2x2)
-6x + 7x2 + 3x3 = (2 * x + 5x * x + 2x2 * x)
-6x + 7x2 + 3x3 = (2x + 5x2 + 2x3)

Solving
-6x + 7x2 + 3x3 = 2x + 5x2 + 2x3

Solving for variable 'x'.

Reorder the terms:
-6x + -2x + 7x2 + -5x2 + 3x3 + -2x3 = 2x + 5x2 + 2x3 + -2x + -5x2 + -2x3

Combine like terms: -6x + -2x = -8x
-8x + 7x2 + -5x2 + 3x3 + -2x3 = 2x + 5x2 + 2x3 + -2x + -5x2 + -2x3

Combine like terms: 7x2 + -5x2 = 2x2
-8x + 2x2 + 3x3 + -2x3 = 2x + 5x2 + 2x3 + -2x + -5x2 + -2x3

Combine like terms: 3x3 + -2x3 = 1x3
-8x + 2x2 + 1x3 = 2x + 5x2 + 2x3 + -2x + -5x2 + -2x3

Reorder the terms:
-8x + 2x2 + 1x3 = 2x + -2x + 5x2 + -5x2 + 2x3 + -2x3

Combine like terms: 2x + -2x = 0
-8x + 2x2 + 1x3 = 0 + 5x2 + -5x2 + 2x3 + -2x3
-8x + 2x2 + 1x3 = 5x2 + -5x2 + 2x3 + -2x3

Combine like terms: 5x2 + -5x2 = 0
-8x + 2x2 + 1x3 = 0 + 2x3 + -2x3
-8x + 2x2 + 1x3 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
-8x + 2x2 + 1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + 2x + x2) = 0

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

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

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

Subproblem 3

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {0, -4, 2}

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