21a^2+57a+30=0

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Solution for 21a^2+57a+30=0 equation:


Simplifying
21a2 + 57a + 30 = 0

Reorder the terms:
30 + 57a + 21a2 = 0

Solving
30 + 57a + 21a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + 19a + 7a2) = 0

Factor a trinomial.
3((2 + a)(5 + 7a)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(2 + a)' equal to zero and attempt to solve: Simplifying 2 + a = 0 Solving 2 + a = 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 + a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + a = 0 + -2 a = 0 + -2 Combine like terms: 0 + -2 = -2 a = -2 Simplifying a = -2

Subproblem 2

Set the factor '(5 + 7a)' equal to zero and attempt to solve: Simplifying 5 + 7a = 0 Solving 5 + 7a = 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 + 7a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7a = 0 + -5 7a = 0 + -5 Combine like terms: 0 + -5 = -5 7a = -5 Divide each side by '7'. a = -0.7142857143 Simplifying a = -0.7142857143

Solution

a = {-2, -0.7142857143}

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