(a-2)(a+1)=10

Solution for (a-2)(a+1)=10 equation:

Simplifying
(a + -2)(a + 1) = 10

Reorder the terms:
(-2 + a)(a + 1) = 10

Reorder the terms:
(-2 + a)(1 + a) = 10

Multiply (-2 + a) * (1 + a)
(-2(1 + a) + a(1 + a)) = 10
((1 * -2 + a * -2) + a(1 + a)) = 10
((-2 + -2a) + a(1 + a)) = 10
(-2 + -2a + (1 * a + a * a)) = 10
(-2 + -2a + (1a + a2)) = 10

Combine like terms: -2a + 1a = -1a
(-2 + -1a + a2) = 10

Solving
-2 + -1a + a2 = 10

Solving for variable 'a'.

Reorder the terms:
-2 + -10 + -1a + a2 = 10 + -10

Combine like terms: -2 + -10 = -12
-12 + -1a + a2 = 10 + -10

Combine like terms: 10 + -10 = 0
-12 + -1a + a2 = 0

Factor a trinomial.
(-3 + -1a)(4 + -1a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-3, 4}