f(a)=a^3+4a^2-32a

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Solution for f(a)=a^3+4a^2-32a equation:


Simplifying
f(a) = a3 + 4a2 + -32a

Multiply f * a
af = a3 + 4a2 + -32a

Reorder the terms:
af = -32a + 4a2 + a3

Solving
af = -32a + 4a2 + a3

Solving for variable 'a'.

Reorder the terms:
32a + af + -4a2 + -1a3 = -32a + 4a2 + a3 + 32a + -4a2 + -1a3

Reorder the terms:
32a + af + -4a2 + -1a3 = -32a + 32a + 4a2 + -4a2 + a3 + -1a3

Combine like terms: -32a + 32a = 0
32a + af + -4a2 + -1a3 = 0 + 4a2 + -4a2 + a3 + -1a3
32a + af + -4a2 + -1a3 = 4a2 + -4a2 + a3 + -1a3

Combine like terms: 4a2 + -4a2 = 0
32a + af + -4a2 + -1a3 = 0 + a3 + -1a3
32a + af + -4a2 + -1a3 = a3 + -1a3

Combine like terms: a3 + -1a3 = 0
32a + af + -4a2 + -1a3 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(32 + f + -4a + -1a2) = 0

Subproblem 1

Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0

Subproblem 2

Set the factor '(32 + f + -4a + -1a2)' equal to zero and attempt to solve: Simplifying 32 + f + -4a + -1a2 = 0 Reorder the terms: 32 + -4a + -1a2 + f = 0 Solving 32 + -4a + -1a2 + f = 0 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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