10a^2+6a^3-3a^3-5a^2-3a^2-7a^4=

Solution for 10a^2+6a^3-3a^3-5a^2-3a^2-7a^4= equation:

Simplifying
10a2 + 6a3 + -3a3 + -5a2 + -3a2 + -7a4 = 0

Reorder the terms:
10a2 + -5a2 + -3a2 + 6a3 + -3a3 + -7a4 = 0

Combine like terms: 10a2 + -5a2 = 5a2
5a2 + -3a2 + 6a3 + -3a3 + -7a4 = 0

Combine like terms: 5a2 + -3a2 = 2a2
2a2 + 6a3 + -3a3 + -7a4 = 0

Combine like terms: 6a3 + -3a3 = 3a3
2a2 + 3a3 + -7a4 = 0

Solving
2a2 + 3a3 + -7a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(2 + 3a + -7a2) = 0

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(2 + 3a + -7a2)' equal to zero and attempt to solve:

Simplifying
2 + 3a + -7a2 = 0

Solving
2 + 3a + -7a2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.2857142857 + -0.4285714286a + a2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -0.4285714286a + 0.2857142857 + a2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -0.4285714286a + a2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -0.4285714286a + a2 = 0 + 0.2857142857
-0.4285714286a + a2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-0.4285714286a + a2 = 0.2857142857

The a term is -0.4285714286a.  Take half its coefficient (-0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
-0.4285714286a + 0.04591836735 + a2 = 0.2857142857 + 0.04591836735

Reorder the terms:
0.04591836735 + -0.4285714286a + a2 = 0.2857142857 + 0.04591836735

Combine like terms: 0.2857142857 + 0.04591836735 = 0.33163265305
0.04591836735 + -0.4285714286a + a2 = 0.33163265305

Factor a perfect square on the left side:
(a + -0.2142857143)(a + -0.2142857143) = 0.33163265305

Calculate the square root of the right side: 0.575875553

Break this problem into two subproblems by setting 
(a + -0.2142857143) equal to 0.575875553 and -0.575875553.

Subproblem 1
a + -0.2142857143 = 0.575875553

Simplifying
a + -0.2142857143 = 0.575875553

Reorder the terms:
-0.2142857143 + a = 0.575875553

Solving
-0.2142857143 + a = 0.575875553

Solving for variable 'a'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + a = 0.575875553 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + a = 0.575875553 + 0.2142857143
a = 0.575875553 + 0.2142857143

Combine like terms: 0.575875553 + 0.2142857143 = 0.7901612673
a = 0.7901612673

Simplifying
a = 0.7901612673

Subproblem 2
a + -0.2142857143 = -0.575875553

Simplifying
a + -0.2142857143 = -0.575875553

Reorder the terms:
-0.2142857143 + a = -0.575875553

Solving
-0.2142857143 + a = -0.575875553

Solving for variable 'a'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + a = -0.575875553 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + a = -0.575875553 + 0.2142857143
a = -0.575875553 + 0.2142857143

Combine like terms: -0.575875553 + 0.2142857143 = -0.3615898387
a = -0.3615898387

Simplifying
a = -0.3615898387

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.7901612673, -0.3615898387}
Solution
a = {0, 0.7901612673, -0.3615898387}