(2a-3b)(4a-2b)=

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Solution for (2a-3b)(4a-2b)= equation: 


Simplifying
(2a + -3b)(4a + -2b) = 0

Multiply (2a + -3b) * (4a + -2b)
(2a * (4a + -2b) + -3b * (4a + -2b)) = 0
((4a * 2a + -2b * 2a) + -3b * (4a + -2b)) = 0

Reorder the terms:
((-4ab + 8a2) + -3b * (4a + -2b)) = 0
((-4ab + 8a2) + -3b * (4a + -2b)) = 0
(-4ab + 8a2 + (4a * -3b + -2b * -3b)) = 0
(-4ab + 8a2 + (-12ab + 6b2)) = 0

Reorder the terms:
(-4ab + -12ab + 8a2 + 6b2) = 0

Combine like terms: -4ab + -12ab = -16ab
(-16ab + 8a2 + 6b2) = 0

Solving
-16ab + 8a2 + 6b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8ab + 4a2 + 3b2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(2a + -3b)' equal to zero and attempt to solve:

Simplifying
2a + -3b = 0

Solving
2a + -3b = 0

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

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

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

Divide each side by '2'.
a = 1.5b

Simplifying
a = 1.5b

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

Simplifying
2a + -1b = 0

Solving
2a + -1b = 0

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

Add 'b' to each side of the equation.
2a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
2a + 0 = 0 + b
2a = 0 + b
Remove the zero:
2a = b

Divide each side by '2'.
a = 0.5b

Simplifying
a = 0.5b
Solution
a = {1.5b, 0.5b}

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