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

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

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

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

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

Multiply (-3 + x) * (3 + 2x)
0 = (-3(3 + 2x) + x(3 + 2x)) + -1x(x + -3)
0 = ((3 * -3 + 2x * -3) + x(3 + 2x)) + -1x(x + -3)
0 = ((-9 + -6x) + x(3 + 2x)) + -1x(x + -3)
0 = (-9 + -6x + (3 * x + 2x * x)) + -1x(x + -3)
0 = (-9 + -6x + (3x + 2x2)) + -1x(x + -3)

Combine like terms: -6x + 3x = -3x
0 = (-9 + -3x + 2x2) + -1x(x + -3)

Reorder the terms:
0 = -9 + -3x + 2x2 + -1x(-3 + x)
0 = -9 + -3x + 2x2 + (-3 * -1x + x * -1x)
0 = -9 + -3x + 2x2 + (3x + -1x2)

Reorder the terms:
0 = -9 + -3x + 3x + 2x2 + -1x2

Combine like terms: -3x + 3x = 0
0 = -9 + 0 + 2x2 + -1x2
0 = -9 + 2x2 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
0 = -9 + 1x2

Solving
0 = -9 + 1x2

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.
0 + -1x2 = -9 + 1x2 + -1x2
Remove the zero:
-1x2 = -9 + 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-1x2 = -9 + 0
-1x2 = -9

Divide each side by '-1'.
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}