(2a+3b)*(5a-b)=

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Solution for (2a+3b)*(5a-b)= equation:


Simplifying
(2a + 3b)(5a + -1b) = 0

Multiply (2a + 3b) * (5a + -1b)
(2a * (5a + -1b) + 3b * (5a + -1b)) = 0
((5a * 2a + -1b * 2a) + 3b * (5a + -1b)) = 0

Reorder the terms:
((-2ab + 10a2) + 3b * (5a + -1b)) = 0
((-2ab + 10a2) + 3b * (5a + -1b)) = 0
(-2ab + 10a2 + (5a * 3b + -1b * 3b)) = 0
(-2ab + 10a2 + (15ab + -3b2)) = 0

Reorder the terms:
(-2ab + 15ab + 10a2 + -3b2) = 0

Combine like terms: -2ab + 15ab = 13ab
(13ab + 10a2 + -3b2) = 0

Solving
13ab + 10a2 + -3b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + -1b)(2a + 3b) = 0

Subproblem 1

Set the factor '(5a + -1b)' equal to zero and attempt to solve: Simplifying 5a + -1b = 0 Solving 5a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 5a + -1b + b = 0 + b Combine like terms: -1b + b = 0 5a + 0 = 0 + b 5a = 0 + b Remove the zero: 5a = b Divide each side by '5'. a = 0.2b Simplifying a = 0.2b

Subproblem 2

Set the factor '(2a + 3b)' equal to zero and attempt to solve: Simplifying 2a + 3b = 0 Solving 2a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 2a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 2a + 0 = 0 + -3b 2a = 0 + -3b Remove the zero: 2a = -3b Divide each side by '2'. a = -1.5b Simplifying a = -1.5b

Solution

a = {0.2b, -1.5b}

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