(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.
(-5 + -1x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-5, 6}