(3a+7)(-4a-5)=0

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Solution for (3a+7)(-4a-5)=0 equation: 


Simplifying
(3a + 7)(-4a + -5) = 0

Reorder the terms:
(7 + 3a)(-4a + -5) = 0

Reorder the terms:
(7 + 3a)(-5 + -4a) = 0

Multiply (7 + 3a) * (-5 + -4a)
(7(-5 + -4a) + 3a * (-5 + -4a)) = 0
((-5 * 7 + -4a * 7) + 3a * (-5 + -4a)) = 0
((-35 + -28a) + 3a * (-5 + -4a)) = 0
(-35 + -28a + (-5 * 3a + -4a * 3a)) = 0
(-35 + -28a + (-15a + -12a2)) = 0

Combine like terms: -28a + -15a = -43a
(-35 + -43a + -12a2) = 0

Solving
-35 + -43a + -12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + 43a + 12a2) = 0

Factor a trinomial.
-1((7 + 3a)(5 + 4a)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + 3a)' equal to zero and attempt to solve:

Simplifying
7 + 3a = 0

Solving
7 + 3a = 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 + 3a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3a = 0 + -7
3a = 0 + -7

Combine like terms: 0 + -7 = -7
3a = -7

Divide each side by '3'.
a = -2.333333333

Simplifying
a = -2.333333333

Subproblem 2
Set the factor '(5 + 4a)' equal to zero and attempt to solve:

Simplifying
5 + 4a = 0

Solving
5 + 4a = 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 + 4a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4a = 0 + -5
4a = 0 + -5

Combine like terms: 0 + -5 = -5
4a = -5

Divide each side by '4'.
a = -1.25

Simplifying
a = -1.25
Solution
a = {-2.333333333, -1.25}

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