(x-1)*(2x+3)=3

Solution for (x-1)*(2x+3)=3 equation:

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

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

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

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

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

Solving
-3 + 1x + 2x2 = 3

Solving for variable 'x'.

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

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

Combine like terms: 3 + -3 = 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}