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

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


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

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

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

Reorder the terms:
(2ab + -3ab + 2a2 + -3b2) = 0

Combine like terms: 2ab + -3ab = -1ab
(-1ab + 2a2 + -3b2) = 0

Solving
-1ab + 2a2 + -3b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -3b)(a + b) = 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 '(a + b)' equal to zero and attempt to solve:

Simplifying
a + b = 0

Solving
a + b = 0

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

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

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

Simplifying
a = -1b
Solution
a = {1.5b, -1b}

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