d^2+3d+1.50=11.50

Solution for d^2+3d+1.50=11.50 equation:

Simplifying
d2 + 3d + 1.50 = 11.50

Reorder the terms:
1.50 + 3d + d2 = 11.50

Solving
1.50 + 3d + d2 = 11.50

Solving for variable 'd'.

Reorder the terms:
1.50 + -11.50 + 3d + d2 = 11.50 + -11.50

Combine like terms: 1.50 + -11.50 = -10
-10 + 3d + d2 = 11.50 + -11.50

Combine like terms: 11.50 + -11.50 = 0.00
-10 + 3d + d2 = 0.00

Factor a trinomial.
(-5 + -1d)(2 + -1d) = 0.00

Subproblem 1
Set the factor '(-5 + -1d)' equal to zero and attempt to solve:

Simplifying
-5 + -1d = 0

Solving
-5 + -1d = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1d = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1d = 0 + 5
-1d = 0 + 5

Combine like terms: 0 + 5 = 5
-1d = 5

Divide each side by '-1'.
d = -5

Simplifying
d = -5
Subproblem 2
Set the factor '(2 + -1d)' equal to zero and attempt to solve:

Simplifying
2 + -1d = 0

Solving
2 + -1d = 0

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

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

Combine like terms: 2 + -2 = 0
0 + -1d = 0 + -2
-1d = 0 + -2

Combine like terms: 0 + -2 = -2
-1d = -2

Divide each side by '-1'.
d = 2

Simplifying
d = 2
Solution
d = {-5, 2}