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Simplifying (5t + -6y)(t + -4y) = 0 Multiply (5t + -6y) * (t + -4y) (5t * (t + -4y) + -6y * (t + -4y)) = 0 ((t * 5t + -4y * 5t) + -6y * (t + -4y)) = 0 Reorder the terms: ((-20ty + 5t2) + -6y * (t + -4y)) = 0 ((-20ty + 5t2) + -6y * (t + -4y)) = 0 (-20ty + 5t2 + (t * -6y + -4y * -6y)) = 0 (-20ty + 5t2 + (-6ty + 24y2)) = 0 Reorder the terms: (-20ty + -6ty + 5t2 + 24y2) = 0 Combine like terms: -20ty + -6ty = -26ty (-26ty + 5t2 + 24y2) = 0 Solving -26ty + 5t2 + 24y2 = 0 Solving for variable 't'. Factor a trinomial. (t + -4y)(5t + -6y) = 0Subproblem 1
Set the factor '(t + -4y)' equal to zero and attempt to solve: Simplifying t + -4y = 0 Solving t + -4y = 0 Move all terms containing t to the left, all other terms to the right. Add '4y' to each side of the equation. t + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 t + 0 = 0 + 4y t = 0 + 4y Remove the zero: t = 4y Simplifying t = 4ySubproblem 2
Set the factor '(5t + -6y)' equal to zero and attempt to solve: Simplifying 5t + -6y = 0 Solving 5t + -6y = 0 Move all terms containing t to the left, all other terms to the right. Add '6y' to each side of the equation. 5t + -6y + 6y = 0 + 6y Combine like terms: -6y + 6y = 0 5t + 0 = 0 + 6y 5t = 0 + 6y Remove the zero: 5t = 6y Divide each side by '5'. t = 1.2y Simplifying t = 1.2ySolution
t = {4y, 1.2y}
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