(2b+3)(b-4)=0

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Solution for (2b+3)(b-4)=0 equation:


Simplifying
(2b + 3)(b + -4) = 0

Reorder the terms:
(3 + 2b)(b + -4) = 0

Reorder the terms:
(3 + 2b)(-4 + b) = 0

Multiply (3 + 2b) * (-4 + b)
(3(-4 + b) + 2b * (-4 + b)) = 0
((-4 * 3 + b * 3) + 2b * (-4 + b)) = 0
((-12 + 3b) + 2b * (-4 + b)) = 0
(-12 + 3b + (-4 * 2b + b * 2b)) = 0
(-12 + 3b + (-8b + 2b2)) = 0

Combine like terms: 3b + -8b = -5b
(-12 + -5b + 2b2) = 0

Solving
-12 + -5b + 2b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-3 + -2b)(4 + -1b) = 0

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 '(4 + -1b)' equal to zero and attempt to solve: Simplifying 4 + -1b = 0 Solving 4 + -1b = 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 + -1b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1b = 0 + -4 -1b = 0 + -4 Combine like terms: 0 + -4 = -4 -1b = -4 Divide each side by '-1'. b = 4 Simplifying b = 4

Solution

b = {-1.5, 4}

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