2a(a+3)(a+10)=0

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Solution for 2a(a+3)(a+10)=0 equation: 


Simplifying
2a(a + 3)(a + 10) = 0

Reorder the terms:
2a(3 + a)(a + 10) = 0

Reorder the terms:
2a(3 + a)(10 + a) = 0

Multiply (3 + a) * (10 + a)
2a(3(10 + a) + a(10 + a)) = 0
2a((10 * 3 + a * 3) + a(10 + a)) = 0
2a((30 + 3a) + a(10 + a)) = 0
2a(30 + 3a + (10 * a + a * a)) = 0
2a(30 + 3a + (10a + a2)) = 0

Combine like terms: 3a + 10a = 13a
2a(30 + 13a + a2) = 0
(30 * 2a + 13a * 2a + a2 * 2a) = 0
(60a + 26a2 + 2a3) = 0

Solving
60a + 26a2 + 2a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(30 + 13a + a2) = 0

Factor a trinomial.
2a((10 + a)(3 + 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 '(10 + a)' equal to zero and attempt to solve:

Simplifying
10 + a = 0

Solving
10 + a = 0

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

Add '-10' to each side of the equation.
10 + -10 + a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + a = 0 + -10
a = 0 + -10

Combine like terms: 0 + -10 = -10
a = -10

Simplifying
a = -10

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

Simplifying
3 + a = 0

Solving
3 + a = 0

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

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

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

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

Simplifying
a = -3
Solution
a = {0, -10, -3}

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