(3b-4)(6b+5)=0

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Solution for (3b-4)(6b+5)=0 equation:


Simplifying
(3b + -4)(6b + 5) = 0

Reorder the terms:
(-4 + 3b)(6b + 5) = 0

Reorder the terms:
(-4 + 3b)(5 + 6b) = 0

Multiply (-4 + 3b) * (5 + 6b)
(-4(5 + 6b) + 3b * (5 + 6b)) = 0
((5 * -4 + 6b * -4) + 3b * (5 + 6b)) = 0
((-20 + -24b) + 3b * (5 + 6b)) = 0
(-20 + -24b + (5 * 3b + 6b * 3b)) = 0
(-20 + -24b + (15b + 18b2)) = 0

Combine like terms: -24b + 15b = -9b
(-20 + -9b + 18b2) = 0

Solving
-20 + -9b + 18b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-5 + -6b)(4 + -3b) = 0

Subproblem 1

Set the factor '(-5 + -6b)' equal to zero and attempt to solve: Simplifying -5 + -6b = 0 Solving -5 + -6b = 0 Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -6b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6b = 0 + 5 -6b = 0 + 5 Combine like terms: 0 + 5 = 5 -6b = 5 Divide each side by '-6'. b = -0.8333333333 Simplifying b = -0.8333333333

Subproblem 2

Set the factor '(4 + -3b)' equal to zero and attempt to solve: Simplifying 4 + -3b = 0 Solving 4 + -3b = 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 + -3b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3b = 0 + -4 -3b = 0 + -4 Combine like terms: 0 + -4 = -4 -3b = -4 Divide each side by '-3'. b = 1.333333333 Simplifying b = 1.333333333

Solution

b = {-0.8333333333, 1.333333333}

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