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

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

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

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

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

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

Combine like terms: -1x + 4x = 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.
(-6 + -1x)(3 + -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 '(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
Solution
x = {-6, 3}