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

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


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

Reorder the terms:
(2a + -5b)(-2a + 3b) = 0

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

Reorder the terms:
((6ab + -4a2) + -5b * (-2a + 3b)) = 0
((6ab + -4a2) + -5b * (-2a + 3b)) = 0
(6ab + -4a2 + (-2a * -5b + 3b * -5b)) = 0
(6ab + -4a2 + (10ab + -15b2)) = 0

Reorder the terms:
(6ab + 10ab + -4a2 + -15b2) = 0

Combine like terms: 6ab + 10ab = 16ab
(16ab + -4a2 + -15b2) = 0

Solving
16ab + -4a2 + -15b2 = 0

Solving for variable 'a'.

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


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 + -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
Solution
a = {1.5b, 2.5b}

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