(a+2)(a+4)=(2a-1)(a+6)

Solution for (a+2)(a+4)=(2a-1)(a+6) equation:

Simplifying
(a + 2)(a + 4) = (2a + -1)(a + 6)

Reorder the terms:
(2 + a)(a + 4) = (2a + -1)(a + 6)

Reorder the terms:
(2 + a)(4 + a) = (2a + -1)(a + 6)

Multiply (2 + a) * (4 + a)
(2(4 + a) + a(4 + a)) = (2a + -1)(a + 6)
((4 * 2 + a * 2) + a(4 + a)) = (2a + -1)(a + 6)
((8 + 2a) + a(4 + a)) = (2a + -1)(a + 6)
(8 + 2a + (4 * a + a * a)) = (2a + -1)(a + 6)
(8 + 2a + (4a + a2)) = (2a + -1)(a + 6)

Combine like terms: 2a + 4a = 6a
(8 + 6a + a2) = (2a + -1)(a + 6)

Reorder the terms:
8 + 6a + a2 = (-1 + 2a)(a + 6)

Reorder the terms:
8 + 6a + a2 = (-1 + 2a)(6 + a)

Multiply (-1 + 2a) * (6 + a)
8 + 6a + a2 = (-1(6 + a) + 2a * (6 + a))
8 + 6a + a2 = ((6 * -1 + a * -1) + 2a * (6 + a))
8 + 6a + a2 = ((-6 + -1a) + 2a * (6 + a))
8 + 6a + a2 = (-6 + -1a + (6 * 2a + a * 2a))
8 + 6a + a2 = (-6 + -1a + (12a + 2a2))

Combine like terms: -1a + 12a = 11a
8 + 6a + a2 = (-6 + 11a + 2a2)

Solving
8 + 6a + a2 = -6 + 11a + 2a2

Solving for variable 'a'.

Reorder the terms:
8 + 6 + 6a + -11a + a2 + -2a2 = -6 + 11a + 2a2 + 6 + -11a + -2a2

Combine like terms: 8 + 6 = 14
14 + 6a + -11a + a2 + -2a2 = -6 + 11a + 2a2 + 6 + -11a + -2a2

Combine like terms: 6a + -11a = -5a
14 + -5a + a2 + -2a2 = -6 + 11a + 2a2 + 6 + -11a + -2a2

Combine like terms: a2 + -2a2 = -1a2
14 + -5a + -1a2 = -6 + 11a + 2a2 + 6 + -11a + -2a2

Reorder the terms:
14 + -5a + -1a2 = -6 + 6 + 11a + -11a + 2a2 + -2a2

Combine like terms: -6 + 6 = 0
14 + -5a + -1a2 = 0 + 11a + -11a + 2a2 + -2a2
14 + -5a + -1a2 = 11a + -11a + 2a2 + -2a2

Combine like terms: 11a + -11a = 0
14 + -5a + -1a2 = 0 + 2a2 + -2a2
14 + -5a + -1a2 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
14 + -5a + -1a2 = 0

Factor a trinomial.
(2 + -1a)(7 + a) = 0

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Subproblem 2
Set the factor '(7 + a)' equal to zero and attempt to solve:

Simplifying
7 + a = 0

Solving
7 + a = 0

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

Add '-7' to each side of the equation.
7 + -7 + a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + a = 0 + -7
a = 0 + -7

Combine like terms: 0 + -7 = -7
a = -7

Simplifying
a = -7
Solution
a = {2, -7}