12-3d=-3d(d-4)

Solution for 12-3d=-3d(d-4) equation:

Simplifying
12 + -3d = -3d(d + -4)

Reorder the terms:
12 + -3d = -3d(-4 + d)
12 + -3d = (-4 * -3d + d * -3d)
12 + -3d = (12d + -3d2)

Solving
12 + -3d = 12d + -3d2

Solving for variable 'd'.

Combine like terms: -3d + -12d = -15d
12 + -15d + 3d2 = 12d + -3d2 + -12d + 3d2

Reorder the terms:
12 + -15d + 3d2 = 12d + -12d + -3d2 + 3d2

Combine like terms: 12d + -12d = 0
12 + -15d + 3d2 = 0 + -3d2 + 3d2
12 + -15d + 3d2 = -3d2 + 3d2

Combine like terms: -3d2 + 3d2 = 0
12 + -15d + 3d2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -5d + d2) = 0

Factor a trinomial.
3((1 + -1d)(4 + -1d)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -1d)' equal to zero and attempt to solve:

Simplifying
1 + -1d = 0

Solving
1 + -1d = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1d = 0 + -1
-1d = 0 + -1

Combine like terms: 0 + -1 = -1
-1d = -1

Divide each side by '-1'.
d = 1

Simplifying
d = 1
Subproblem 2
Set the factor '(4 + -1d)' equal to zero and attempt to solve:

Simplifying
4 + -1d = 0

Solving
4 + -1d = 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 + -1d = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1d = 0 + -4
-1d = 0 + -4

Combine like terms: 0 + -4 = -4
-1d = -4

Divide each side by '-1'.
d = 4

Simplifying
d = 4
Solution
d = {1, 4}