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

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


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

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

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

Multiply (-3 + 4b) * (-5 + 3b)
(-3(-5 + 3b) + 4b * (-5 + 3b)) = 0
((-5 * -3 + 3b * -3) + 4b * (-5 + 3b)) = 0
((15 + -9b) + 4b * (-5 + 3b)) = 0
(15 + -9b + (-5 * 4b + 3b * 4b)) = 0
(15 + -9b + (-20b + 12b2)) = 0

Combine like terms: -9b + -20b = -29b
(15 + -29b + 12b2) = 0

Solving
15 + -29b + 12b2 = 0

Solving for variable 'b'.

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

Subproblem 1

Set the factor '(3 + -4b)' equal to zero and attempt to solve: Simplifying 3 + -4b = 0 Solving 3 + -4b = 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 + -4b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4b = 0 + -3 -4b = 0 + -3 Combine like terms: 0 + -3 = -3 -4b = -3 Divide each side by '-4'. b = 0.75 Simplifying b = 0.75

Subproblem 2

Set the factor '(5 + -3b)' equal to zero and attempt to solve: Simplifying 5 + -3b = 0 Solving 5 + -3b = 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 + -3b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3b = 0 + -5 -3b = 0 + -5 Combine like terms: 0 + -5 = -5 -3b = -5 Divide each side by '-3'. b = 1.666666667 Simplifying b = 1.666666667

Solution

b = {0.75, 1.666666667}

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