3a^2+12a-45=0

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Solution for 3a^2+12a-45=0 equation: 


Simplifying
3a2 + 12a + -45 = 0

Reorder the terms:
-45 + 12a + 3a2 = 0

Solving
-45 + 12a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 4a + a2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-15 + 4a + a2)' equal to zero and attempt to solve:

Simplifying
-15 + 4a + a2 = 0

Solving
-15 + 4a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 4a + 15 + a2 = 0 + 15

Reorder the terms:
-15 + 15 + 4a + a2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 4a + a2 = 0 + 15
4a + a2 = 0 + 15

Combine like terms: 0 + 15 = 15
4a + a2 = 15

The a term is 4a.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4a + 4 + a2 = 15 + 4

Reorder the terms:
4 + 4a + a2 = 15 + 4

Combine like terms: 15 + 4 = 19
4 + 4a + a2 = 19

Factor a perfect square on the left side:
(a + 2)(a + 2) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(a + 2) equal to 4.358898944 and -4.358898944.


Subproblem 1
a + 2 = 4.358898944

Simplifying
a + 2 = 4.358898944

Reorder the terms:
2 + a = 4.358898944

Solving
2 + a = 4.358898944

Solving for variable 'a'.

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

Add '-2' to each side of the equation.
2 + -2 + a = 4.358898944 + -2

Combine like terms: 2 + -2 = 0
0 + a = 4.358898944 + -2
a = 4.358898944 + -2

Combine like terms: 4.358898944 + -2 = 2.358898944
a = 2.358898944

Simplifying
a = 2.358898944


Subproblem 2
a + 2 = -4.358898944

Simplifying
a + 2 = -4.358898944

Reorder the terms:
2 + a = -4.358898944

Solving
2 + a = -4.358898944

Solving for variable 'a'.

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

Add '-2' to each side of the equation.
2 + -2 + a = -4.358898944 + -2

Combine like terms: 2 + -2 = 0
0 + a = -4.358898944 + -2
a = -4.358898944 + -2

Combine like terms: -4.358898944 + -2 = -6.358898944
a = -6.358898944

Simplifying
a = -6.358898944


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.358898944, -6.358898944}
Solution
a = {2.358898944, -6.358898944}

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