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

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


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

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

Reorder the terms for easier multiplication:
-5 * 5(2a + -3b)(-2a + 3b) = 0

Multiply -5 * 5
-25(2a + -3b)(-2a + 3b) = 0

Multiply (2a + -3b) * (-2a + 3b)
-25(2a * (-2a + 3b) + -3b * (-2a + 3b)) = 0
-25((-2a * 2a + 3b * 2a) + -3b * (-2a + 3b)) = 0

Reorder the terms:
-25((6ab + -4a2) + -3b * (-2a + 3b)) = 0
-25((6ab + -4a2) + -3b * (-2a + 3b)) = 0
-25(6ab + -4a2 + (-2a * -3b + 3b * -3b)) = 0
-25(6ab + -4a2 + (6ab + -9b2)) = 0

Reorder the terms:
-25(6ab + 6ab + -4a2 + -9b2) = 0

Combine like terms: 6ab + 6ab = 12ab
-25(12ab + -4a2 + -9b2) = 0
(12ab * -25 + -4a2 * -25 + -9b2 * -25) = 0
(-300ab + 100a2 + 225b2) = 0

Solving
-300ab + 100a2 + 225b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '25'.
25(-12ab + 4a2 + 9b2) = 0

Factor a trinomial.
25((2a + -3b)(2a + -3b)) = 0

Ignore the factor 25.

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

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