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Simplifying 15(2x2 + -1y2) = 7xy (2x2 * 15 + -1y2 * 15) = 7xy (30x2 + -15y2) = 7xy Solving 30x2 + -15y2 = 7xy Solving for variable 'x'. Reorder the terms: -7xy + 30x2 + -15y2 = 7xy + -7xy Combine like terms: 7xy + -7xy = 0 -7xy + 30x2 + -15y2 = 0 Factor a trinomial. (6x + -5y)(5x + 3y) = 0Subproblem 1
Set the factor '(6x + -5y)' equal to zero and attempt to solve: Simplifying 6x + -5y = 0 Solving 6x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 6x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 6x + 0 = 0 + 5y 6x = 0 + 5y Remove the zero: 6x = 5y Divide each side by '6'. x = 0.8333333333y Simplifying x = 0.8333333333ySubproblem 2
Set the factor '(5x + 3y)' equal to zero and attempt to solve: Simplifying 5x + 3y = 0 Solving 5x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 5x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 5x + 0 = 0 + -3y 5x = 0 + -3y Remove the zero: 5x = -3y Divide each side by '5'. x = -0.6y Simplifying x = -0.6ySolution
x = {0.8333333333y, -0.6y}
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