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

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

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

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

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

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

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

Solving
-6 + 1x + 2x2 = -3

Solving for variable 'x'.

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

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-1.5, 1}