10b^2-15b=8b-12

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Solution for 10b^2-15b=8b-12 equation:


Simplifying
10b2 + -15b = 8b + -12

Reorder the terms:
-15b + 10b2 = 8b + -12

Reorder the terms:
-15b + 10b2 = -12 + 8b

Solving
-15b + 10b2 = -12 + 8b

Solving for variable 'b'.

Reorder the terms:
12 + -15b + -8b + 10b2 = -12 + 8b + 12 + -8b

Combine like terms: -15b + -8b = -23b
12 + -23b + 10b2 = -12 + 8b + 12 + -8b

Reorder the terms:
12 + -23b + 10b2 = -12 + 12 + 8b + -8b

Combine like terms: -12 + 12 = 0
12 + -23b + 10b2 = 0 + 8b + -8b
12 + -23b + 10b2 = 8b + -8b

Combine like terms: 8b + -8b = 0
12 + -23b + 10b2 = 0

Factor a trinomial.
(4 + -5b)(3 + -2b) = 0

Subproblem 1

Set the factor '(4 + -5b)' equal to zero and attempt to solve: Simplifying 4 + -5b = 0 Solving 4 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5b = 0 + -4 -5b = 0 + -4 Combine like terms: 0 + -4 = -4 -5b = -4 Divide each side by '-5'. b = 0.8 Simplifying b = 0.8

Subproblem 2

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

Solution

b = {0.8, 1.5}

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