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

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


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

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

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

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

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

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

Add '2' to each side of the equation.
-2 + 1x + 2 + 6x2 = -2 + 2 + x

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

Combine like terms: -2 + 2 = 0
0 + 1x + 6x2 = -2 + 2 + x
1x + 6x2 = -2 + 2 + x

Combine like terms: -2 + 2 = 0
1x + 6x2 = 0 + x
1x + 6x2 = x

Solving
1x + 6x2 = x

Solving for variable 'x'.

Reorder the terms:
1x + -1x + 6x2 = x + -1x

Combine like terms: 1x + -1x = 0
0 + 6x2 = x + -1x
6x2 = x + -1x

Combine like terms: x + -1x = 0
6x2 = 0

Ignore the factor 6.

Subproblem 1

Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}

Solution

x = {0}

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