2(3a-7)(5a-6)=

Solution for 2(3a-7)(5a-6)= equation:

Simplifying
2(3a + -7)(5a + -6) = 0

Reorder the terms:
2(-7 + 3a)(5a + -6) = 0

Reorder the terms:
2(-7 + 3a)(-6 + 5a) = 0

Multiply (-7 + 3a) * (-6 + 5a)
2(-7(-6 + 5a) + 3a * (-6 + 5a)) = 0
2((-6 * -7 + 5a * -7) + 3a * (-6 + 5a)) = 0
2((42 + -35a) + 3a * (-6 + 5a)) = 0
2(42 + -35a + (-6 * 3a + 5a * 3a)) = 0
2(42 + -35a + (-18a + 15a2)) = 0

Combine like terms: -35a + -18a = -53a
2(42 + -53a + 15a2) = 0
(42 * 2 + -53a * 2 + 15a2 * 2) = 0
(84 + -106a + 30a2) = 0

Solving
84 + -106a + 30a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(42 + -53a + 15a2) = 0

Factor a trinomial.
2((6 + -5a)(7 + -3a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -5a)' equal to zero and attempt to solve:

Simplifying
6 + -5a = 0

Solving
6 + -5a = 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 + -5a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5a = 0 + -6
-5a = 0 + -6

Combine like terms: 0 + -6 = -6
-5a = -6

Divide each side by '-5'.
a = 1.2

Simplifying
a = 1.2
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 = {1.2, 2.333333333}