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

Solution for (3a-7)(4a+5)= 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 = -13a
(-35 + -13a + 12a2) = 0

Solving
-35 + -13a + 12a2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
Subproblem 2
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
Solution
a = {-1.25, 2.333333333}