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

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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}

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