a^2+5a+10=3a+-6

Solution for a^2+5a+10=3a+-6 equation:

Simplifying
a2 + 5a + 10 = 3a + -6

Reorder the terms:
10 + 5a + a2 = 3a + -6

Reorder the terms:
10 + 5a + a2 = -6 + 3a

Solving
10 + 5a + a2 = -6 + 3a

Solving for variable 'a'.

Reorder the terms:
10 + 6 + 5a + -3a + a2 = -6 + 3a + 6 + -3a

Combine like terms: 10 + 6 = 16
16 + 5a + -3a + a2 = -6 + 3a + 6 + -3a

Combine like terms: 5a + -3a = 2a
16 + 2a + a2 = -6 + 3a + 6 + -3a

Reorder the terms:
16 + 2a + a2 = -6 + 6 + 3a + -3a

Combine like terms: -6 + 6 = 0
16 + 2a + a2 = 0 + 3a + -3a
16 + 2a + a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
16 + 2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 2a + -16 + a2 = 0 + -16

Reorder the terms:
16 + -16 + 2a + a2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 2a + a2 = 0 + -16
2a + a2 = 0 + -16

Combine like terms: 0 + -16 = -16
2a + a2 = -16

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 = -16 + 1

Reorder the terms:
1 + 2a + a2 = -16 + 1

Combine like terms: -16 + 1 = -15
1 + 2a + a2 = -15

Factor a perfect square on the left side:
(a + 1)(a + 1) = -15

Can't calculate square root of the right side.

The solution to this equation could not be determined.