5(a+3)=3*1-a*a

Solution for 5(a+3)=3*1-a*a equation:

Simplifying
5(a + 3) = 3 * 1 + -1a * a

Reorder the terms:
5(3 + a) = 3 * 1 + -1a * a
(3 * 5 + a * 5) = 3 * 1 + -1a * a
(15 + 5a) = 3 * 1 + -1a * a

Multiply 3 * 1
15 + 5a = 3 + -1a * a

Multiply a * a
15 + 5a = 3 + -1a2

Solving
15 + 5a = 3 + -1a2

Solving for variable 'a'.

Reorder the terms:
15 + -3 + 5a + a2 = 3 + -1a2 + -3 + a2

Combine like terms: 15 + -3 = 12
12 + 5a + a2 = 3 + -1a2 + -3 + a2

Reorder the terms:
12 + 5a + a2 = 3 + -3 + -1a2 + a2

Combine like terms: 3 + -3 = 0
12 + 5a + a2 = 0 + -1a2 + a2
12 + 5a + a2 = -1a2 + a2

Combine like terms: -1a2 + a2 = 0
12 + 5a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 5a + -12 + a2 = 0 + -12

Reorder the terms:
12 + -12 + 5a + a2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 5a + a2 = 0 + -12
5a + a2 = 0 + -12

Combine like terms: 0 + -12 = -12
5a + a2 = -12

The a term is 5a.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5a + 6.25 + a2 = -12 + 6.25

Reorder the terms:
6.25 + 5a + a2 = -12 + 6.25

Combine like terms: -12 + 6.25 = -5.75
6.25 + 5a + a2 = -5.75

Factor a perfect square on the left side:
(a + 2.5)(a + 2.5) = -5.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.