3d(3d-4)(4d+9)=0

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Solution for 3d(3d-4)(4d+9)=0 equation: 


Simplifying
3d(3d + -4)(4d + 9) = 0

Reorder the terms:
3d(-4 + 3d)(4d + 9) = 0

Reorder the terms:
3d(-4 + 3d)(9 + 4d) = 0

Multiply (-4 + 3d) * (9 + 4d)
3d(-4(9 + 4d) + 3d * (9 + 4d)) = 0
3d((9 * -4 + 4d * -4) + 3d * (9 + 4d)) = 0
3d((-36 + -16d) + 3d * (9 + 4d)) = 0
3d(-36 + -16d + (9 * 3d + 4d * 3d)) = 0
3d(-36 + -16d + (27d + 12d2)) = 0

Combine like terms: -16d + 27d = 11d
3d(-36 + 11d + 12d2) = 0
(-36 * 3d + 11d * 3d + 12d2 * 3d) = 0
(-108d + 33d2 + 36d3) = 0

Solving
-108d + 33d2 + 36d3 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '3d'.
3d(-36 + 11d + 12d2) = 0

Factor a trinomial.
3d((-9 + -4d)(4 + -3d)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'd' equal to zero and attempt to solve:

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0

Subproblem 2
Set the factor '(-9 + -4d)' equal to zero and attempt to solve:

Simplifying
-9 + -4d = 0

Solving
-9 + -4d = 0

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

Add '9' to each side of the equation.
-9 + 9 + -4d = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4d = 0 + 9
-4d = 0 + 9

Combine like terms: 0 + 9 = 9
-4d = 9

Divide each side by '-4'.
d = -2.25

Simplifying
d = -2.25

Subproblem 3
Set the factor '(4 + -3d)' equal to zero and attempt to solve:

Simplifying
4 + -3d = 0

Solving
4 + -3d = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3d = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3d = 0 + -4
-3d = 0 + -4

Combine like terms: 0 + -4 = -4
-3d = -4

Divide each side by '-3'.
d = 1.333333333

Simplifying
d = 1.333333333
Solution
d = {0, -2.25, 1.333333333}

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