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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

Combine like terms: 1x + -1x = 0
-6 + 0 + 2x2 = 3 + x + -3 + -1x
-6 + 2x2 = 3 + x + -3 + -1x

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

Combine like terms: 3 + -3 = 0
-6 + 2x2 = 0 + x + -1x
-6 + 2x2 = x + -1x

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + x2)' equal to zero and attempt to solve:

Simplifying
-3 + x2 = 0

Solving
-3 + x2 = 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 + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x2 = 0 + 3
x2 = 0 + 3

Combine like terms: 0 + 3 = 3
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {-1.732050808, 1.732050808}