(5a+3)(7a-6)=

Solution for (5a+3)(7a-6)= equation:

Simplifying
(5a + 3)(7a + -6) = 0

Reorder the terms:
(3 + 5a)(7a + -6) = 0

Reorder the terms:
(3 + 5a)(-6 + 7a) = 0

Multiply (3 + 5a) * (-6 + 7a)
(3(-6 + 7a) + 5a * (-6 + 7a)) = 0
((-6 * 3 + 7a * 3) + 5a * (-6 + 7a)) = 0
((-18 + 21a) + 5a * (-6 + 7a)) = 0
(-18 + 21a + (-6 * 5a + 7a * 5a)) = 0
(-18 + 21a + (-30a + 35a2)) = 0

Combine like terms: 21a + -30a = -9a
(-18 + -9a + 35a2) = 0

Solving
-18 + -9a + 35a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -5a)(6 + -7a) = 0

Subproblem 1
Set the factor '(-3 + -5a)' equal to zero and attempt to solve:

Simplifying
-3 + -5a = 0

Solving
-3 + -5a = 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 + -5a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5a = 0 + 3
-5a = 0 + 3

Combine like terms: 0 + 3 = 3
-5a = 3

Divide each side by '-5'.
a = -0.6

Simplifying
a = -0.6
Subproblem 2
Set the factor '(6 + -7a)' equal to zero and attempt to solve:

Simplifying
6 + -7a = 0

Solving
6 + -7a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7a = 0 + -6
-7a = 0 + -6

Combine like terms: 0 + -6 = -6
-7a = -6

Divide each side by '-7'.
a = 0.8571428571

Simplifying
a = 0.8571428571
Solution
a = {-0.6, 0.8571428571}