(3a+43)(2a+37)=

Solution for (3a+43)(2a+37)= equation:

Simplifying
(3a + 43)(2a + 37) = 0

Reorder the terms:
(43 + 3a)(2a + 37) = 0

Reorder the terms:
(43 + 3a)(37 + 2a) = 0

Multiply (43 + 3a) * (37 + 2a)
(43(37 + 2a) + 3a * (37 + 2a)) = 0
((37 * 43 + 2a * 43) + 3a * (37 + 2a)) = 0
((1591 + 86a) + 3a * (37 + 2a)) = 0
(1591 + 86a + (37 * 3a + 2a * 3a)) = 0
(1591 + 86a + (111a + 6a2)) = 0

Combine like terms: 86a + 111a = 197a
(1591 + 197a + 6a2) = 0

Solving
1591 + 197a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(37 + 2a)(43 + 3a) = 0

Subproblem 1
Set the factor '(37 + 2a)' equal to zero and attempt to solve:

Simplifying
37 + 2a = 0

Solving
37 + 2a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-37' to each side of the equation.
37 + -37 + 2a = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 2a = 0 + -37
2a = 0 + -37

Combine like terms: 0 + -37 = -37
2a = -37

Divide each side by '2'.
a = -18.5

Simplifying
a = -18.5
Subproblem 2
Set the factor '(43 + 3a)' equal to zero and attempt to solve:

Simplifying
43 + 3a = 0

Solving
43 + 3a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-43' to each side of the equation.
43 + -43 + 3a = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 3a = 0 + -43
3a = 0 + -43

Combine like terms: 0 + -43 = -43
3a = -43

Divide each side by '3'.
a = -14.33333333

Simplifying
a = -14.33333333
Solution
a = {-18.5, -14.33333333}