(12a-3b)(2a-5b)=

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Solution for (12a-3b)(2a-5b)= equation: 


Simplifying
(12a + -3b)(2a + -5b) = 0

Multiply (12a + -3b) * (2a + -5b)
(12a * (2a + -5b) + -3b * (2a + -5b)) = 0
((2a * 12a + -5b * 12a) + -3b * (2a + -5b)) = 0

Reorder the terms:
((-60ab + 24a2) + -3b * (2a + -5b)) = 0
((-60ab + 24a2) + -3b * (2a + -5b)) = 0
(-60ab + 24a2 + (2a * -3b + -5b * -3b)) = 0
(-60ab + 24a2 + (-6ab + 15b2)) = 0

Reorder the terms:
(-60ab + -6ab + 24a2 + 15b2) = 0

Combine like terms: -60ab + -6ab = -66ab
(-66ab + 24a2 + 15b2) = 0

Solving
-66ab + 24a2 + 15b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-22ab + 8a2 + 5b2) = 0

Factor a trinomial.
3((2a + -5b)(4a + -1b)) = 0

Ignore the factor 3.

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

Simplifying
2a + -5b = 0

Solving
2a + -5b = 0

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

Add '5b' to each side of the equation.
2a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
2a + 0 = 0 + 5b
2a = 0 + 5b
Remove the zero:
2a = 5b

Divide each side by '2'.
a = 2.5b

Simplifying
a = 2.5b

Subproblem 2
Set the factor '(4a + -1b)' equal to zero and attempt to solve:

Simplifying
4a + -1b = 0

Solving
4a + -1b = 0

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

Add 'b' to each side of the equation.
4a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
4a + 0 = 0 + b
4a = 0 + b
Remove the zero:
4a = b

Divide each side by '4'.
a = 0.25b

Simplifying
a = 0.25b
Solution
a = {2.5b, 0.25b}

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