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

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


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

Subproblem 3
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
Solution
a = {0, 1.4, -0.6666666667}

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