3a(7a-2b)+2b(7a-2b)=0

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Solution for 3a(7a-2b)+2b(7a-2b)=0 equation: 


Simplifying
3a(7a + -2b) + 2b(7a + -2b) = 0
(7a * 3a + -2b * 3a) + 2b(7a + -2b) = 0

Reorder the terms:
(-6ab + 21a2) + 2b(7a + -2b) = 0
(-6ab + 21a2) + 2b(7a + -2b) = 0
-6ab + 21a2 + (7a * 2b + -2b * 2b) = 0
-6ab + 21a2 + (14ab + -4b2) = 0

Reorder the terms:
-6ab + 14ab + 21a2 + -4b2 = 0

Combine like terms: -6ab + 14ab = 8ab
8ab + 21a2 + -4b2 = 0

Solving
8ab + 21a2 + -4b2 = 0

Solving for variable 'a'.

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


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

Simplifying
7a + -2b = 0

Solving
7a + -2b = 0

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

Add '2b' to each side of the equation.
7a + -2b + 2b = 0 + 2b

Combine like terms: -2b + 2b = 0
7a + 0 = 0 + 2b
7a = 0 + 2b
Remove the zero:
7a = 2b

Divide each side by '7'.
a = 0.2857142857b

Simplifying
a = 0.2857142857b

Subproblem 2
Set the factor '(3a + 2b)' equal to zero and attempt to solve:

Simplifying
3a + 2b = 0

Solving
3a + 2b = 0

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

Add '-2b' to each side of the equation.
3a + 2b + -2b = 0 + -2b

Combine like terms: 2b + -2b = 0
3a + 0 = 0 + -2b
3a = 0 + -2b
Remove the zero:
3a = -2b

Divide each side by '3'.
a = -0.6666666667b

Simplifying
a = -0.6666666667b
Solution
a = {0.2857142857b, -0.6666666667b}

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