(4a-b)(9a+5b)=

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Solution for (4a-b)(9a+5b)= equation:


Simplifying
(4a + -1b)(9a + 5b) = 0

Multiply (4a + -1b) * (9a + 5b)
(4a * (9a + 5b) + -1b * (9a + 5b)) = 0
((9a * 4a + 5b * 4a) + -1b * (9a + 5b)) = 0

Reorder the terms:
((20ab + 36a2) + -1b * (9a + 5b)) = 0
((20ab + 36a2) + -1b * (9a + 5b)) = 0
(20ab + 36a2 + (9a * -1b + 5b * -1b)) = 0
(20ab + 36a2 + (-9ab + -5b2)) = 0

Reorder the terms:
(20ab + -9ab + 36a2 + -5b2) = 0

Combine like terms: 20ab + -9ab = 11ab
(11ab + 36a2 + -5b2) = 0

Solving
11ab + 36a2 + -5b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + -1b)(9a + 5b) = 0

Subproblem 1

Set the factor '(4a + -1b)' equal to zero and attempt to solve: Simplifying 4a + -1b = 0 Solving 4a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 4a + -1b + b = 0 + b Combine like terms: -1b + b = 0 4a + 0 = 0 + b 4a = 0 + b Remove the zero: 4a = b Divide each side by '4'. a = 0.25b Simplifying a = 0.25b

Subproblem 2

Set the factor '(9a + 5b)' equal to zero and attempt to solve: Simplifying 9a + 5b = 0 Solving 9a + 5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. 9a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 9a + 0 = 0 + -5b 9a = 0 + -5b Remove the zero: 9a = -5b Divide each side by '9'. a = -0.5555555556b Simplifying a = -0.5555555556b

Solution

a = {0.25b, -0.5555555556b}

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