4a+6=(a+2)*(a+4)

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

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

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

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

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

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

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

Solving
6 + 4a = 8 + 6a + a2

Solving for variable 'a'.

Reorder the terms:
6 + -8 + 4a + -6a + -1a2 = 8 + 6a + a2 + -8 + -6a + -1a2

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

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

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

Combine like terms: 8 + -8 = 0
-2 + -2a + -1a2 = 0 + 6a + -6a + a2 + -1a2
-2 + -2a + -1a2 = 6a + -6a + a2 + -1a2

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 2a + a2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 2a + a2)' equal to zero and attempt to solve:

Simplifying
2 + 2a + a2 = 0

Solving
2 + 2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 2a + -2 + a2 = 0 + -2

Reorder the terms:
2 + -2 + 2a + a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2a + a2 = 0 + -2
2a + a2 = 0 + -2

Combine like terms: 0 + -2 = -2
2a + a2 = -2

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = -2 + 1

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

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

Factor a perfect square on the left side:
(a + 1)(a + 1) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.