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

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


Simplifying
-2(a + -5)(a2 + 7a) = 0

Reorder the terms:
-2(-5 + a)(a2 + 7a) = 0

Reorder the terms:
-2(-5 + a)(7a + a2) = 0

Multiply (-5 + a) * (7a + a2)
-2(-5(7a + a2) + a(7a + a2)) = 0
-2((7a * -5 + a2 * -5) + a(7a + a2)) = 0
-2((-35a + -5a2) + a(7a + a2)) = 0
-2(-35a + -5a2 + (7a * a + a2 * a)) = 0
-2(-35a + -5a2 + (7a2 + a3)) = 0

Combine like terms: -5a2 + 7a2 = 2a2
-2(-35a + 2a2 + a3) = 0
(-35a * -2 + 2a2 * -2 + a3 * -2) = 0
(70a + -4a2 + -2a3) = 0

Solving
70a + -4a2 + -2a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(35 + -2a + -1a2) = 0

Factor a trinomial.
2a((5 + -1a)(7 + a)) = 0

Ignore the factor 2.

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 '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5

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

Simplifying
7 + a = 0

Solving
7 + a = 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 + a = 0 + -7

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

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

Simplifying
a = -7
Solution
a = {0, 5, -7}

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