-3b(4b-10)=.5(-24+60)

Solution for -3b(4b-10)=.5(-24+60) equation:

Simplifying
-3b(4b + -10) = 0.5(-24 + 60)

Reorder the terms:
-3b(-10 + 4b) = 0.5(-24 + 60)
(-10 * -3b + 4b * -3b) = 0.5(-24 + 60)
(30b + -12b2) = 0.5(-24 + 60)

Combine like terms: -24 + 60 = 36
30b + -12b2 = 0.5(36)

Multiply 0.5 * 36
30b + -12b2 = 18

Solving
30b + -12b2 = 18

Solving for variable 'b'.

Reorder the terms:
-18 + 30b + -12b2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 30b + -12b2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + 5b + -2b2) = 0

Factor a trinomial.
6((-3 + 2b)(1 + -1b)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + 2b)' equal to zero and attempt to solve:

Simplifying
-3 + 2b = 0

Solving
-3 + 2b = 0

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

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

Combine like terms: -3 + 3 = 0
0 + 2b = 0 + 3
2b = 0 + 3

Combine like terms: 0 + 3 = 3
2b = 3

Divide each side by '2'.
b = 1.5

Simplifying
b = 1.5
Subproblem 2
Set the factor '(1 + -1b)' equal to zero and attempt to solve:

Simplifying
1 + -1b = 0

Solving
1 + -1b = 0

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

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

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

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

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

Simplifying
b = 1
Solution
b = {1.5, 1}