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

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


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

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

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

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

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

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

Solving
-6x + 3x2 = -2 + -3x + 2x2

Solving for variable 'x'.

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

Combine like terms: -6x + 3x = -3x
2 + -3x + 3x2 + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2

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

Reorder the terms:
2 + -3x + 1x2 = -2 + 2 + -3x + 3x + 2x2 + -2x2

Combine like terms: -2 + 2 = 0
2 + -3x + 1x2 = 0 + -3x + 3x + 2x2 + -2x2
2 + -3x + 1x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
2 + -3x + 1x2 = 0 + 2x2 + -2x2
2 + -3x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
2 + -3x + 1x2 = 0

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

Subproblem 1

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

Subproblem 2

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 = {1, 2}

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