a(5a-7)(4a+7)=0

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Solution for a(5a-7)(4a+7)=0 equation: 


Simplifying
a(5a + -7)(4a + 7) = 0

Reorder the terms:
a(-7 + 5a)(4a + 7) = 0

Reorder the terms:
a(-7 + 5a)(7 + 4a) = 0

Multiply (-7 + 5a) * (7 + 4a)
a(-7(7 + 4a) + 5a * (7 + 4a)) = 0
a((7 * -7 + 4a * -7) + 5a * (7 + 4a)) = 0
a((-49 + -28a) + 5a * (7 + 4a)) = 0
a(-49 + -28a + (7 * 5a + 4a * 5a)) = 0
a(-49 + -28a + (35a + 20a2)) = 0

Combine like terms: -28a + 35a = 7a
a(-49 + 7a + 20a2) = 0
(-49 * a + 7a * a + 20a2 * a) = 0
(-49a + 7a2 + 20a3) = 0

Solving
-49a + 7a2 + 20a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-49 + 7a + 20a2) = 0

Factor a trinomial.
a((-7 + -4a)(7 + -5a)) = 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 '(-7 + -4a)' equal to zero and attempt to solve:

Simplifying
-7 + -4a = 0

Solving
-7 + -4a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -4a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4a = 0 + 7
-4a = 0 + 7

Combine like terms: 0 + 7 = 7
-4a = 7

Divide each side by '-4'.
a = -1.75

Simplifying
a = -1.75

Subproblem 3
Set the factor '(7 + -5a)' equal to zero and attempt to solve:

Simplifying
7 + -5a = 0

Solving
7 + -5a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5a = 0 + -7
-5a = 0 + -7

Combine like terms: 0 + -7 = -7
-5a = -7

Divide each side by '-5'.
a = 1.4

Simplifying
a = 1.4
Solution
a = {0, -1.75, 1.4}

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