a(a+15)+(a+30)+(a+60-1)=

Solution for a(a+15)+(a+30)+(a+60-1)= equation:

Simplifying
a(a + 15) + (a + 30) + (a + 60 + -1) = 0

Reorder the terms:
a(15 + a) + (a + 30) + (a + 60 + -1) = 0
(15 * a + a * a) + (a + 30) + (a + 60 + -1) = 0
(15a + a2) + (a + 30) + (a + 60 + -1) = 0

Reorder the terms:
15a + a2 + (30 + a) + (a + 60 + -1) = 0

Remove parenthesis around (30 + a)
15a + a2 + 30 + a + (a + 60 + -1) = 0

Reorder the terms:
15a + a2 + 30 + a + (60 + -1 + a) = 0

Combine like terms: 60 + -1 = 59
15a + a2 + 30 + a + (59 + a) = 0

Remove parenthesis around (59 + a)
15a + a2 + 30 + a + 59 + a = 0

Reorder the terms:
30 + 59 + 15a + a + a + a2 = 0

Combine like terms: 30 + 59 = 89
89 + 15a + a + a + a2 = 0

Combine like terms: 15a + a = 16a
89 + 16a + a + a2 = 0

Combine like terms: 16a + a = 17a
89 + 17a + a2 = 0

Solving
89 + 17a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-89' to each side of the equation.
89 + 17a + -89 + a2 = 0 + -89

Reorder the terms:
89 + -89 + 17a + a2 = 0 + -89

Combine like terms: 89 + -89 = 0
0 + 17a + a2 = 0 + -89
17a + a2 = 0 + -89

Combine like terms: 0 + -89 = -89
17a + a2 = -89

The a term is 17a.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17a + 72.25 + a2 = -89 + 72.25

Reorder the terms:
72.25 + 17a + a2 = -89 + 72.25

Combine like terms: -89 + 72.25 = -16.75
72.25 + 17a + a2 = -16.75

Factor a perfect square on the left side:
(a + 8.5)(a + 8.5) = -16.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.