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

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

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

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

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

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

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

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

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

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

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

Solving
-6 + 2x2 = x2

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

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

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

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

Add '6' to each side of the equation.
-6 + 6 + 1x2 = 0 + 6

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

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

Divide each side by '1'.
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}