(3f^2+4f-9)+(6f-3+f^2)=

Solution for (3f^2+4f-9)+(6f-3+f^2)= equation:

Simplifying
(3f2 + 4f + -9) + (6f + -3 + f2) = 0

Reorder the terms:
(-9 + 4f + 3f2) + (6f + -3 + f2) = 0

Remove parenthesis around (-9 + 4f + 3f2)
-9 + 4f + 3f2 + (6f + -3 + f2) = 0

Reorder the terms:
-9 + 4f + 3f2 + (-3 + 6f + f2) = 0

Remove parenthesis around (-3 + 6f + f2)
-9 + 4f + 3f2 + -3 + 6f + f2 = 0

Reorder the terms:
-9 + -3 + 4f + 6f + 3f2 + f2 = 0

Combine like terms: -9 + -3 = -12
-12 + 4f + 6f + 3f2 + f2 = 0

Combine like terms: 4f + 6f = 10f
-12 + 10f + 3f2 + f2 = 0

Combine like terms: 3f2 + f2 = 4f2
-12 + 10f + 4f2 = 0

Solving
-12 + 10f + 4f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 5f + 2f2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 5f + 2f2)' equal to zero and attempt to solve:

Simplifying
-6 + 5f + 2f2 = 0

Solving
-6 + 5f + 2f2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-3 + 2.5f + f2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 2.5f + 3 + f2 = 0 + 3

Reorder the terms:
-3 + 3 + 2.5f + f2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2.5f + f2 = 0 + 3
2.5f + f2 = 0 + 3

Combine like terms: 0 + 3 = 3
2.5f + f2 = 3

The f term is 2.5f.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5f + 1.5625 + f2 = 3 + 1.5625

Reorder the terms:
1.5625 + 2.5f + f2 = 3 + 1.5625

Combine like terms: 3 + 1.5625 = 4.5625
1.5625 + 2.5f + f2 = 4.5625

Factor a perfect square on the left side:
(f + 1.25)(f + 1.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(f + 1.25) equal to 2.136000936 and -2.136000936.

Subproblem 1
f + 1.25 = 2.136000936

Simplifying
f + 1.25 = 2.136000936

Reorder the terms:
1.25 + f = 2.136000936

Solving
1.25 + f = 2.136000936

Solving for variable 'f'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + f = 2.136000936 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + f = 2.136000936 + -1.25
f = 2.136000936 + -1.25

Combine like terms: 2.136000936 + -1.25 = 0.886000936
f = 0.886000936

Simplifying
f = 0.886000936

Subproblem 2
f + 1.25 = -2.136000936

Simplifying
f + 1.25 = -2.136000936

Reorder the terms:
1.25 + f = -2.136000936

Solving
1.25 + f = -2.136000936

Solving for variable 'f'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + f = -2.136000936 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + f = -2.136000936 + -1.25
f = -2.136000936 + -1.25

Combine like terms: -2.136000936 + -1.25 = -3.386000936
f = -3.386000936

Simplifying
f = -3.386000936

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {0.886000936, -3.386000936}
Solution
f = {0.886000936, -3.386000936}