a(5a-7)(3a+2)=

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Solution for a(5a-7)(3a+2)= equation: 


Simplifying
a(5a + -7)(3a + 2) = 0

Reorder the terms:
a(-7 + 5a)(3a + 2) = 0

Reorder the terms:
a(-7 + 5a)(2 + 3a) = 0

Multiply (-7 + 5a) * (2 + 3a)
a(-7(2 + 3a) + 5a * (2 + 3a)) = 0
a((2 * -7 + 3a * -7) + 5a * (2 + 3a)) = 0
a((-14 + -21a) + 5a * (2 + 3a)) = 0
a(-14 + -21a + (2 * 5a + 3a * 5a)) = 0
a(-14 + -21a + (10a + 15a2)) = 0

Combine like terms: -21a + 10a = -11a
a(-14 + -11a + 15a2) = 0
(-14 * a + -11a * a + 15a2 * a) = 0
(-14a + -11a2 + 15a3) = 0

Solving
-14a + -11a2 + 15a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-14 + -11a + 15a2) = 0

Factor a trinomial.
a((-2 + -3a)(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 '(-2 + -3a)' equal to zero and attempt to solve:

Simplifying
-2 + -3a = 0

Solving
-2 + -3a = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3a = 0 + 2
-3a = 0 + 2

Combine like terms: 0 + 2 = 2
-3a = 2

Divide each side by '-3'.
a = -0.6666666667

Simplifying
a = -0.6666666667

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, -0.6666666667, 1.4}

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