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

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

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

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

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

Multiply (-1 + a) * (4 + a)
(-1(4 + a) + a(4 + a)) = 14
((4 * -1 + a * -1) + a(4 + a)) = 14
((-4 + -1a) + a(4 + a)) = 14
(-4 + -1a + (4 * a + a * a)) = 14
(-4 + -1a + (4a + a2)) = 14

Combine like terms: -1a + 4a = 3a
(-4 + 3a + a2) = 14

Solving
-4 + 3a + a2 = 14

Solving for variable 'a'.

Reorder the terms:
-4 + -14 + 3a + a2 = 14 + -14

Combine like terms: -4 + -14 = -18
-18 + 3a + a2 = 14 + -14

Combine like terms: 14 + -14 = 0
-18 + 3a + a2 = 0

Factor a trinomial.
(-6 + -1a)(3 + -1a) = 0

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

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

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

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

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

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

Simplifying
a = -6
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

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

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

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

Simplifying
a = 3
Solution
a = {-6, 3}