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

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

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

Reorder the terms:
2x(3 + x) + -1(x + 2)(x + -3) = 0
(3 * 2x + x * 2x) + -1(x + 2)(x + -3) = 0
(6x + 2x2) + -1(x + 2)(x + -3) = 0

Reorder the terms:
6x + 2x2 + -1(2 + x)(x + -3) = 0

Reorder the terms:
6x + 2x2 + -1(2 + x)(-3 + x) = 0

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

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

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

Combine like terms: 6x + 1x = 7x
6 + 7x + 2x2 + -1x2 = 0

Combine like terms: 2x2 + -1x2 = 1x2
6 + 7x + 1x2 = 0

Solving
6 + 7x + 1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + x)(1 + x) = 0

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

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

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

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

Simplifying
x = -6
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-6, -1}