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

Solution for (7a+5)(2a-6)=0 equation:

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

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

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

Multiply (5 + 7a) * (-6 + 2a)
(5(-6 + 2a) + 7a * (-6 + 2a)) = 0
((-6 * 5 + 2a * 5) + 7a * (-6 + 2a)) = 0
((-30 + 10a) + 7a * (-6 + 2a)) = 0
(-30 + 10a + (-6 * 7a + 2a * 7a)) = 0
(-30 + 10a + (-42a + 14a2)) = 0

Combine like terms: 10a + -42a = -32a
(-30 + -32a + 14a2) = 0

Solving
-30 + -32a + 14a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -16a + 7a2) = 0

Factor a trinomial.
2((-5 + -7a)(3 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -7a)' equal to zero and attempt to solve:

Simplifying
-5 + -7a = 0

Solving
-5 + -7a = 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 + -7a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7a = 0 + 5
-7a = 0 + 5

Combine like terms: 0 + 5 = 5
-7a = 5

Divide each side by '-7'.
a = -0.7142857143

Simplifying
a = -0.7142857143
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.7142857143, 3}