(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

Add '3' to each side of the equation.
-3 + -1x + 3 + 2x2 = -3 + 3

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

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

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

Solving
-1x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 2x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 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 + 2x = 0 + 1

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

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

Divide each side by '2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, 0.5}