(12a+7)(5a-15)=0

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Solution for (12a+7)(5a-15)=0 equation:


Simplifying
(12a + 7)(5a + -15) = 0

Reorder the terms:
(7 + 12a)(5a + -15) = 0

Reorder the terms:
(7 + 12a)(-15 + 5a) = 0

Multiply (7 + 12a) * (-15 + 5a)
(7(-15 + 5a) + 12a * (-15 + 5a)) = 0
((-15 * 7 + 5a * 7) + 12a * (-15 + 5a)) = 0
((-105 + 35a) + 12a * (-15 + 5a)) = 0
(-105 + 35a + (-15 * 12a + 5a * 12a)) = 0
(-105 + 35a + (-180a + 60a2)) = 0

Combine like terms: 35a + -180a = -145a
(-105 + -145a + 60a2) = 0

Solving
-105 + -145a + 60a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + -29a + 12a2) = 0

Factor a trinomial.
5((-7 + -12a)(3 + -1a)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-7 + -12a)' equal to zero and attempt to solve: Simplifying -7 + -12a = 0 Solving -7 + -12a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -12a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -12a = 0 + 7 -12a = 0 + 7 Combine like terms: 0 + 7 = 7 -12a = 7 Divide each side by '-12'. a = -0.5833333333 Simplifying a = -0.5833333333

Subproblem 2

Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 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 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3

Solution

a = {-0.5833333333, 3}

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