(14a+5b)(7a-6b)=0

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Solution for (14a+5b)(7a-6b)=0 equation: 


Simplifying
(14a + 5b)(7a + -6b) = 0

Multiply (14a + 5b) * (7a + -6b)
(14a * (7a + -6b) + 5b * (7a + -6b)) = 0
((7a * 14a + -6b * 14a) + 5b * (7a + -6b)) = 0

Reorder the terms:
((-84ab + 98a2) + 5b * (7a + -6b)) = 0
((-84ab + 98a2) + 5b * (7a + -6b)) = 0
(-84ab + 98a2 + (7a * 5b + -6b * 5b)) = 0
(-84ab + 98a2 + (35ab + -30b2)) = 0

Reorder the terms:
(-84ab + 35ab + 98a2 + -30b2) = 0

Combine like terms: -84ab + 35ab = -49ab
(-49ab + 98a2 + -30b2) = 0

Solving
-49ab + 98a2 + -30b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(7a + -6b)(14a + 5b) = 0


Subproblem 1
Set the factor '(7a + -6b)' equal to zero and attempt to solve:

Simplifying
7a + -6b = 0

Solving
7a + -6b = 0

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

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

Combine like terms: -6b + 6b = 0
7a + 0 = 0 + 6b
7a = 0 + 6b
Remove the zero:
7a = 6b

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

Simplifying
a = 0.8571428571b

Subproblem 2
Set the factor '(14a + 5b)' equal to zero and attempt to solve:

Simplifying
14a + 5b = 0

Solving
14a + 5b = 0

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

Add '-5b' to each side of the equation.
14a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
14a + 0 = 0 + -5b
14a = 0 + -5b
Remove the zero:
14a = -5b

Divide each side by '14'.
a = -0.3571428571b

Simplifying
a = -0.3571428571b
Solution
a = {0.8571428571b, -0.3571428571b}

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