18a^2+24ag+8g^2=0

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Solution for 18a^2+24ag+8g^2=0 equation:


Simplifying
18a2 + 24ag + 8g2 = 0

Reorder the terms:
24ag + 18a2 + 8g2 = 0

Solving
24ag + 18a2 + 8g2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12ag + 9a2 + 4g2) = 0

Factor a trinomial.
2((3a + 2g)(3a + 2g)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3a + 2g)' equal to zero and attempt to solve: Simplifying 3a + 2g = 0 Solving 3a + 2g = 0 Move all terms containing a to the left, all other terms to the right. Add '-2g' to each side of the equation. 3a + 2g + -2g = 0 + -2g Combine like terms: 2g + -2g = 0 3a + 0 = 0 + -2g 3a = 0 + -2g Remove the zero: 3a = -2g Divide each side by '3'. a = -0.6666666667g Simplifying a = -0.6666666667g

Subproblem 2

Set the factor '(3a + 2g)' equal to zero and attempt to solve: Simplifying 3a + 2g = 0 Solving 3a + 2g = 0 Move all terms containing a to the left, all other terms to the right. Add '-2g' to each side of the equation. 3a + 2g + -2g = 0 + -2g Combine like terms: 2g + -2g = 0 3a + 0 = 0 + -2g 3a = 0 + -2g Remove the zero: 3a = -2g Divide each side by '3'. a = -0.6666666667g Simplifying a = -0.6666666667g

Solution

a = {-0.6666666667g, -0.6666666667g}

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