(2x-3)(x+1)=18

Solution for (2x-3)(x+1)=18 equation:

Simplifying
(2x + -3)(x + 1) = 18

Reorder the terms:
(-3 + 2x)(x + 1) = 18

Reorder the terms:
(-3 + 2x)(1 + x) = 18

Multiply (-3 + 2x) * (1 + x)
(-3(1 + x) + 2x * (1 + x)) = 18
((1 * -3 + x * -3) + 2x * (1 + x)) = 18
((-3 + -3x) + 2x * (1 + x)) = 18
(-3 + -3x + (1 * 2x + x * 2x)) = 18
(-3 + -3x + (2x + 2x2)) = 18

Combine like terms: -3x + 2x = -1x
(-3 + -1x + 2x2) = 18

Solving
-3 + -1x + 2x2 = 18

Solving for variable 'x'.

Reorder the terms:
-3 + -18 + -1x + 2x2 = 18 + -18

Combine like terms: -3 + -18 = -21
-21 + -1x + 2x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-21 + -1x + 2x2 = 0

Factor a trinomial.
(-3 + -1x)(7 + -2x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-3, 3.5}