(x-4)(x+1)=14

Solution for (x-4)(x+1)=14 equation:

Simplifying
(x + -4)(x + 1) = 14

Reorder the terms:
(-4 + x)(x + 1) = 14

Reorder the terms:
(-4 + x)(1 + x) = 14

Multiply (-4 + x) * (1 + x)
(-4(1 + x) + x(1 + x)) = 14
((1 * -4 + x * -4) + x(1 + x)) = 14
((-4 + -4x) + x(1 + x)) = 14
(-4 + -4x + (1 * x + x * x)) = 14
(-4 + -4x + (1x + x2)) = 14

Combine like terms: -4x + 1x = -3x
(-4 + -3x + x2) = 14

Solving
-4 + -3x + x2 = 14

Solving for variable 'x'.

Reorder the terms:
-4 + -14 + -3x + x2 = 14 + -14

Combine like terms: -4 + -14 = -18
-18 + -3x + x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-18 + -3x + x2 = 0

Factor a trinomial.
(-3 + -1x)(6 + -1x) = 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 '(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 = {-3, 6}