10a^2+33a+27=0

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Solution for 10a^2+33a+27=0 equation:


Simplifying
10a2 + 33a + 27 = 0

Reorder the terms:
27 + 33a + 10a2 = 0

Solving
27 + 33a + 10a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(9 + 5a)(3 + 2a) = 0

Subproblem 1

Set the factor '(9 + 5a)' equal to zero and attempt to solve: Simplifying 9 + 5a = 0 Solving 9 + 5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 5a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5a = 0 + -9 5a = 0 + -9 Combine like terms: 0 + -9 = -9 5a = -9 Divide each side by '5'. a = -1.8 Simplifying a = -1.8

Subproblem 2

Set the factor '(3 + 2a)' equal to zero and attempt to solve: Simplifying 3 + 2a = 0 Solving 3 + 2a = 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 + 2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2a = 0 + -3 2a = 0 + -3 Combine like terms: 0 + -3 = -3 2a = -3 Divide each side by '2'. a = -1.5 Simplifying a = -1.5

Solution

a = {-1.8, -1.5}

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