42a^2-12ab-30b^2=

Solution for 42a^2-12ab-30b^2= equation:

Simplifying
42a2 + -12ab + -30b2 = 0

Reorder the terms:
-12ab + 42a2 + -30b2 = 0

Solving
-12ab + 42a2 + -30b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2ab + 7a2 + -5b2) = 0

Factor a trinomial.
6((a + -1b)(7a + 5b)) = 0

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

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

Add 'b' to each side of the equation.
a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
a + 0 = 0 + b
a = 0 + b
Remove the zero:
a = b

Simplifying
a = b
Subproblem 2
Set the factor '(7a + 5b)' equal to zero and attempt to solve:

Simplifying
7a + 5b = 0

Solving
7a + 5b = 0

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

Add '-5b' to each side of the equation.
7a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
7a + 0 = 0 + -5b
7a = 0 + -5b
Remove the zero:
7a = -5b

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

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