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

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


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

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

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

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

Reorder the terms:
((-3ax + -6a2) + 2x * (2a + x)) = 0
((-3ax + -6a2) + 2x * (2a + x)) = 0
(-3ax + -6a2 + (2a * 2x + x * 2x)) = 0
(-3ax + -6a2 + (4ax + 2x2)) = 0

Reorder the terms:
(-3ax + 4ax + -6a2 + 2x2) = 0

Combine like terms: -3ax + 4ax = 1ax
(1ax + -6a2 + 2x2) = 0

Solving
1ax + -6a2 + 2x2 = 0

Solving for variable 'a'.

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


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

Simplifying
-2a + -1x = 0

Solving
-2a + -1x = 0

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

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

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

Divide each side by '-2'.
a = -0.5x

Simplifying
a = -0.5x

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

Simplifying
3a + -2x = 0

Solving
3a + -2x = 0

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

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

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

Divide each side by '3'.
a = 0.6666666667x

Simplifying
a = 0.6666666667x
Solution
a = {-0.5x, 0.6666666667x}

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