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

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

Simplifying
(x + 3)(x + -2) = -1x2

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

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

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

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

Solving
-6 + 1x + x2 = -1x2

Solving for variable 'x'.

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

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

Factor a trinomial.
(-2 + -1x)(3 + -2x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-2, 1.5}