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Simplifying (3a + 2b)(4a + -5b) = 0 Multiply (3a + 2b) * (4a + -5b) (3a * (4a + -5b) + 2b * (4a + -5b)) = 0 ((4a * 3a + -5b * 3a) + 2b * (4a + -5b)) = 0 Reorder the terms: ((-15ab + 12a2) + 2b * (4a + -5b)) = 0 ((-15ab + 12a2) + 2b * (4a + -5b)) = 0 (-15ab + 12a2 + (4a * 2b + -5b * 2b)) = 0 (-15ab + 12a2 + (8ab + -10b2)) = 0 Reorder the terms: (-15ab + 8ab + 12a2 + -10b2) = 0 Combine like terms: -15ab + 8ab = -7ab (-7ab + 12a2 + -10b2) = 0 Solving -7ab + 12a2 + -10b2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + -5b)(3a + 2b) = 0Subproblem 1
Set the factor '(4a + -5b)' equal to zero and attempt to solve: Simplifying 4a + -5b = 0 Solving 4a + -5b = 0 Move all terms containing a to the left, all other terms to the right. Add '5b' to each side of the equation. 4a + -5b + 5b = 0 + 5b Combine like terms: -5b + 5b = 0 4a + 0 = 0 + 5b 4a = 0 + 5b Remove the zero: 4a = 5b Divide each side by '4'. a = 1.25b Simplifying a = 1.25bSubproblem 2
Set the factor '(3a + 2b)' equal to zero and attempt to solve: Simplifying 3a + 2b = 0 Solving 3a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 3a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 3a + 0 = 0 + -2b 3a = 0 + -2b Remove the zero: 3a = -2b Divide each side by '3'. a = -0.6666666667b Simplifying a = -0.6666666667bSolution
a = {1.25b, -0.6666666667b}
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