5a^4-(15a^3)+(35a^2)=0

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Solution for 5a^4-(15a^3)+(35a^2)=0 equation: 


Simplifying
5a4 + -1(15a3) + (35a2) = 0

Remove parenthesis around (15a3)
5a4 + -1 * 15a3 + (35a2) = 0

Multiply -1 * 15
5a4 + -15a3 + (35a2) = 0

Reorder the terms:
(35a2) + -15a3 + 5a4 = 0

Solving
(35a2) + -15a3 + 5a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5a2'.
5a2(7 + -3a + a2) = 0

Ignore the factor 5.

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 '(7 + -3a + a2)' equal to zero and attempt to solve:

Simplifying
7 + -3a + a2 = 0

Solving
7 + -3a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -3a + -7 + a2 = 0 + -7

Reorder the terms:
7 + -7 + -3a + a2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3a + a2 = 0 + -7
-3a + a2 = 0 + -7

Combine like terms: 0 + -7 = -7
-3a + a2 = -7

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 = -7 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -7 + 2.25

Combine like terms: -7 + 2.25 = -4.75
2.25 + -3a + a2 = -4.75

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = -4.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}

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