(3a-4b)(3a-4b)=0

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Solution for (3a-4b)(3a-4b)=0 equation: 


Simplifying
(3a + -4b)(3a + -4b) = 0

Multiply (3a + -4b) * (3a + -4b)
(3a * (3a + -4b) + -4b * (3a + -4b)) = 0
((3a * 3a + -4b * 3a) + -4b * (3a + -4b)) = 0

Reorder the terms:
((-12ab + 9a2) + -4b * (3a + -4b)) = 0
((-12ab + 9a2) + -4b * (3a + -4b)) = 0
(-12ab + 9a2 + (3a * -4b + -4b * -4b)) = 0
(-12ab + 9a2 + (-12ab + 16b2)) = 0

Reorder the terms:
(-12ab + -12ab + 9a2 + 16b2) = 0

Combine like terms: -12ab + -12ab = -24ab
(-24ab + 9a2 + 16b2) = 0

Solving
-24ab + 9a2 + 16b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + -4b)(3a + -4b) = 0


Subproblem 1
Set the factor '(3a + -4b)' equal to zero and attempt to solve:

Simplifying
3a + -4b = 0

Solving
3a + -4b = 0

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

Add '4b' to each side of the equation.
3a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
3a + 0 = 0 + 4b
3a = 0 + 4b
Remove the zero:
3a = 4b

Divide each side by '3'.
a = 1.333333333b

Simplifying
a = 1.333333333b

Subproblem 2
Set the factor '(3a + -4b)' equal to zero and attempt to solve:

Simplifying
3a + -4b = 0

Solving
3a + -4b = 0

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

Add '4b' to each side of the equation.
3a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
3a + 0 = 0 + 4b
3a = 0 + 4b
Remove the zero:
3a = 4b

Divide each side by '3'.
a = 1.333333333b

Simplifying
a = 1.333333333b
Solution
a = {1.333333333b, 1.333333333b}

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