(2x+3)(x-2)-x(x-1)=0

Solution for (2x+3)(x-2)-x(x-1)=0 equation:

Simplifying
(2x + 3)(x + -2) + -1x(x + -1) = 0

Reorder the terms:
(3 + 2x)(x + -2) + -1x(x + -1) = 0

Reorder the terms:
(3 + 2x)(-2 + x) + -1x(x + -1) = 0

Multiply (3 + 2x) * (-2 + x)
(3(-2 + x) + 2x * (-2 + x)) + -1x(x + -1) = 0
((-2 * 3 + x * 3) + 2x * (-2 + x)) + -1x(x + -1) = 0
((-6 + 3x) + 2x * (-2 + x)) + -1x(x + -1) = 0
(-6 + 3x + (-2 * 2x + x * 2x)) + -1x(x + -1) = 0
(-6 + 3x + (-4x + 2x2)) + -1x(x + -1) = 0

Combine like terms: 3x + -4x = -1x
(-6 + -1x + 2x2) + -1x(x + -1) = 0

Reorder the terms:
-6 + -1x + 2x2 + -1x(-1 + x) = 0
-6 + -1x + 2x2 + (-1 * -1x + x * -1x) = 0
-6 + -1x + 2x2 + (1x + -1x2) = 0

Reorder the terms:
-6 + -1x + 1x + 2x2 + -1x2 = 0

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

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

Solving
-6 + 1x2 = 0

Solving for variable 'x'.

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

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}