(10a+2)(12a+9)=0

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Solution for (10a+2)(12a+9)=0 equation:


Simplifying
(10a + 2)(12a + 9) = 0

Reorder the terms:
(2 + 10a)(12a + 9) = 0

Reorder the terms:
(2 + 10a)(9 + 12a) = 0

Multiply (2 + 10a) * (9 + 12a)
(2(9 + 12a) + 10a * (9 + 12a)) = 0
((9 * 2 + 12a * 2) + 10a * (9 + 12a)) = 0
((18 + 24a) + 10a * (9 + 12a)) = 0
(18 + 24a + (9 * 10a + 12a * 10a)) = 0
(18 + 24a + (90a + 120a2)) = 0

Combine like terms: 24a + 90a = 114a
(18 + 114a + 120a2) = 0

Solving
18 + 114a + 120a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + 19a + 20a2) = 0

Factor a trinomial.
6((3 + 4a)(1 + 5a)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(3 + 4a)' equal to zero and attempt to solve: Simplifying 3 + 4a = 0 Solving 3 + 4a = 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 + 4a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4a = 0 + -3 4a = 0 + -3 Combine like terms: 0 + -3 = -3 4a = -3 Divide each side by '4'. a = -0.75 Simplifying a = -0.75

Subproblem 2

Set the factor '(1 + 5a)' equal to zero and attempt to solve: Simplifying 1 + 5a = 0 Solving 1 + 5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 5a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5a = 0 + -1 5a = 0 + -1 Combine like terms: 0 + -1 = -1 5a = -1 Divide each side by '5'. a = -0.2 Simplifying a = -0.2

Solution

a = {-0.75, -0.2}

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