f(-5a)=3(-5a)(-5a-4)

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Solution for f(-5a)=3(-5a)(-5a-4) equation:


Simplifying
f(-5a) = 3(-5a)(-5a + -4)

Remove parenthesis around (-5a)
f * -5a = 3(-5a)(-5a + -4)

Reorder the terms for easier multiplication:
-5f * a = 3(-5a)(-5a + -4)

Multiply f * a
-5af = 3(-5a)(-5a + -4)

Remove parenthesis around (-5a)
-5af = 3 * -5a(-5a + -4)

Reorder the terms:
-5af = 3 * -5a(-4 + -5a)

Multiply 3 * -5
-5af = -15a(-4 + -5a)
-5af = (-4 * -15a + -5a * -15a)
-5af = (60a + 75a2)

Solving
-5af = 60a + 75a2

Solving for variable 'a'.

Reorder the terms:
-60a + -5af + -75a2 = 60a + 75a2 + -60a + -75a2

Reorder the terms:
-60a + -5af + -75a2 = 60a + -60a + 75a2 + -75a2

Combine like terms: 60a + -60a = 0
-60a + -5af + -75a2 = 0 + 75a2 + -75a2
-60a + -5af + -75a2 = 75a2 + -75a2

Combine like terms: 75a2 + -75a2 = 0
-60a + -5af + -75a2 = 0

Factor out the Greatest Common Factor (GCF), '-5a'.
-5a(12 + f + 15a) = 0

Ignore the factor -5.

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 '(12 + f + 15a)' equal to zero and attempt to solve: Simplifying 12 + f + 15a = 0 Reorder the terms: 12 + 15a + f = 0 Solving 12 + 15a + f = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 15a + -12 + f = 0 + -12 Reorder the terms: 12 + -12 + 15a + f = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 15a + f = 0 + -12 15a + f = 0 + -12 Combine like terms: 0 + -12 = -12 15a + f = -12 Add '-1f' to each side of the equation. 15a + f + -1f = -12 + -1f Combine like terms: f + -1f = 0 15a + 0 = -12 + -1f 15a = -12 + -1f Divide each side by '15'. a = -0.8 + -0.06666666667f Simplifying a = -0.8 + -0.06666666667f

Solution

a = {0, -0.8 + -0.06666666667f}

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