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

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Solution for (2a+3b)(5a-2b)=0 equation: 


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

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

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

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

Combine like terms: -4ab + 15ab = 11ab
(11ab + 10a2 + -6b2) = 0

Solving
11ab + 10a2 + -6b2 = 0

Solving for variable 'a'.

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


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

Simplifying
5a + -2b = 0

Solving
5a + -2b = 0

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

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

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

Divide each side by '5'.
a = 0.4b

Simplifying
a = 0.4b

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 = {0.4b, -1.5b}

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