(3a-3d)(3a+2d)=0

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


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

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

Reorder the terms:
((6ad + 9a2) + -3d * (3a + 2d)) = 0
((6ad + 9a2) + -3d * (3a + 2d)) = 0
(6ad + 9a2 + (3a * -3d + 2d * -3d)) = 0
(6ad + 9a2 + (-9ad + -6d2)) = 0

Reorder the terms:
(6ad + -9ad + 9a2 + -6d2) = 0

Combine like terms: 6ad + -9ad = -3ad
(-3ad + 9a2 + -6d2) = 0

Solving
-3ad + 9a2 + -6d2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1ad + 3a2 + -2d2) = 0

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

Ignore the factor 3.

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

Simplifying
a + -1d = 0

Solving
a + -1d = 0

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

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

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

Simplifying
a = d

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

Simplifying
3a + 2d = 0

Solving
3a + 2d = 0

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

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

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

Divide each side by '3'.
a = -0.6666666667d

Simplifying
a = -0.6666666667d
Solution
a = {d, -0.6666666667d}

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