5a(a)+15a-30=

Solution for 5a(a)+15a-30= equation:

Simplifying
5a(a) + 15a + -30 = 0

Multiply a * a
5a2 + 15a + -30 = 0

Reorder the terms:
-30 + 15a + 5a2 = 0

Solving
-30 + 15a + 5a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + 3a + a2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + 3a + a2)' equal to zero and attempt to solve:

Simplifying
-6 + 3a + a2 = 0

Solving
-6 + 3a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3a + 6 + a2 = 0 + 6

Reorder the terms:
-6 + 6 + 3a + a2 = 0 + 6

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

Combine like terms: 0 + 6 = 6
3a + a2 = 6

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = 6 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + 3a + a2 = 8.25

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(a + 1.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
a + 1.5 = 2.872281323

Simplifying
a + 1.5 = 2.872281323

Reorder the terms:
1.5 + a = 2.872281323

Solving
1.5 + a = 2.872281323

Solving for variable 'a'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = 2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = 2.872281323 + -1.5
a = 2.872281323 + -1.5

Combine like terms: 2.872281323 + -1.5 = 1.372281323
a = 1.372281323

Simplifying
a = 1.372281323

Subproblem 2
a + 1.5 = -2.872281323

Simplifying
a + 1.5 = -2.872281323

Reorder the terms:
1.5 + a = -2.872281323

Solving
1.5 + a = -2.872281323

Solving for variable 'a'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = -2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = -2.872281323 + -1.5
a = -2.872281323 + -1.5

Combine like terms: -2.872281323 + -1.5 = -4.372281323
a = -4.372281323

Simplifying
a = -4.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.372281323, -4.372281323}
Solution
a = {1.372281323, -4.372281323}