(a-5)(2a+3)=-11

Solution for (a-5)(2a+3)=-11 equation:

Simplifying
(a + -5)(2a + 3) = -11

Reorder the terms:
(-5 + a)(2a + 3) = -11

Reorder the terms:
(-5 + a)(3 + 2a) = -11

Multiply (-5 + a) * (3 + 2a)
(-5(3 + 2a) + a(3 + 2a)) = -11
((3 * -5 + 2a * -5) + a(3 + 2a)) = -11
((-15 + -10a) + a(3 + 2a)) = -11
(-15 + -10a + (3 * a + 2a * a)) = -11
(-15 + -10a + (3a + 2a2)) = -11

Combine like terms: -10a + 3a = -7a
(-15 + -7a + 2a2) = -11

Solving
-15 + -7a + 2a2 = -11

Solving for variable 'a'.

Reorder the terms:
-15 + 11 + -7a + 2a2 = -11 + 11

Combine like terms: -15 + 11 = -4
-4 + -7a + 2a2 = -11 + 11

Combine like terms: -11 + 11 = 0
-4 + -7a + 2a2 = 0

Factor a trinomial.
(-1 + -2a)(4 + -1a) = 0

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

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2a = 0 + 1
-2a = 0 + 1

Combine like terms: 0 + 1 = 1
-2a = 1

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5
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 = {-0.5, 4}