(x-3)(x+4)=18

Solution for (x-3)(x+4)=18 equation:

Simplifying
(x + -3)(x + 4) = 18

Reorder the terms:
(-3 + x)(x + 4) = 18

Reorder the terms:
(-3 + x)(4 + x) = 18

Multiply (-3 + x) * (4 + x)
(-3(4 + x) + x(4 + x)) = 18
((4 * -3 + x * -3) + x(4 + x)) = 18
((-12 + -3x) + x(4 + x)) = 18
(-12 + -3x + (4 * x + x * x)) = 18
(-12 + -3x + (4x + x2)) = 18

Combine like terms: -3x + 4x = 1x
(-12 + 1x + x2) = 18

Solving
-12 + 1x + x2 = 18

Solving for variable 'x'.

Reorder the terms:
-12 + -18 + 1x + x2 = 18 + -18

Combine like terms: -12 + -18 = -30
-30 + 1x + x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-30 + 1x + x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

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

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

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-6, 5}