(2a-10)(7a-42)=0

Solution for (2a-10)(7a-42)=0 equation:

Simplifying
(2a + -10)(7a + -42) = 0

Reorder the terms:
(-10 + 2a)(7a + -42) = 0

Reorder the terms:
(-10 + 2a)(-42 + 7a) = 0

Multiply (-10 + 2a) * (-42 + 7a)
(-10(-42 + 7a) + 2a * (-42 + 7a)) = 0
((-42 * -10 + 7a * -10) + 2a * (-42 + 7a)) = 0
((420 + -70a) + 2a * (-42 + 7a)) = 0
(420 + -70a + (-42 * 2a + 7a * 2a)) = 0
(420 + -70a + (-84a + 14a2)) = 0

Combine like terms: -70a + -84a = -154a
(420 + -154a + 14a2) = 0

Solving
420 + -154a + 14a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '14'.
14(30 + -11a + a2) = 0

Factor a trinomial.
14((5 + -1a)(6 + -1a)) = 0

Ignore the factor 14.
Subproblem 1
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 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 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

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

Simplifying
6 + -1a = 0

Solving
6 + -1a = 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 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {5, 6}