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Simplifying 0 = (5a + -1b)(2a + 3b) Multiply (5a + -1b) * (2a + 3b) 0 = (5a * (2a + 3b) + -1b * (2a + 3b)) 0 = ((2a * 5a + 3b * 5a) + -1b * (2a + 3b)) Reorder the terms: 0 = ((15ab + 10a2) + -1b * (2a + 3b)) 0 = ((15ab + 10a2) + -1b * (2a + 3b)) 0 = (15ab + 10a2 + (2a * -1b + 3b * -1b)) 0 = (15ab + 10a2 + (-2ab + -3b2)) Reorder the terms: 0 = (15ab + -2ab + 10a2 + -3b2) Combine like terms: 15ab + -2ab = 13ab 0 = (13ab + 10a2 + -3b2) Solving 0 = 13ab + 10a2 + -3b2 Solving for variable 'a'. Remove the zero: -13ab + -10a2 + 3b2 = 13ab + 10a2 + -3b2 + -13ab + -10a2 + 3b2 Reorder the terms: -13ab + -10a2 + 3b2 = 13ab + -13ab + 10a2 + -10a2 + -3b2 + 3b2 Combine like terms: 13ab + -13ab = 0 -13ab + -10a2 + 3b2 = 0 + 10a2 + -10a2 + -3b2 + 3b2 -13ab + -10a2 + 3b2 = 10a2 + -10a2 + -3b2 + 3b2 Combine like terms: 10a2 + -10a2 = 0 -13ab + -10a2 + 3b2 = 0 + -3b2 + 3b2 -13ab + -10a2 + 3b2 = -3b2 + 3b2 Combine like terms: -3b2 + 3b2 = 0 -13ab + -10a2 + 3b2 = 0 Factor a trinomial. (-2a + -3b)(5a + -1b) = 0Subproblem 1
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 = -1.5bSubproblem 2
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 = 0.2bSolution
a = {-1.5b, 0.2b}
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