(x-3)(x+2)=-4

Solution for (x-3)(x+2)=-4 equation:

Simplifying
(x + -3)(x + 2) = -4

Reorder the terms:
(-3 + x)(x + 2) = -4

Reorder the terms:
(-3 + x)(2 + x) = -4

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

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

Solving
-6 + -1x + x2 = -4

Solving for variable 'x'.

Reorder the terms:
-6 + 4 + -1x + x2 = -4 + 4

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

Combine like terms: -4 + 4 = 0
-2 + -1x + x2 = 0

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

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1
Subproblem 2
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
Solution
x = {-1, 2}