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Simplifying (8x + 3y)(4x + 7y) = 0 Multiply (8x + 3y) * (4x + 7y) (8x * (4x + 7y) + 3y * (4x + 7y)) = 0 ((4x * 8x + 7y * 8x) + 3y * (4x + 7y)) = 0 Reorder the terms: ((56xy + 32x2) + 3y * (4x + 7y)) = 0 ((56xy + 32x2) + 3y * (4x + 7y)) = 0 (56xy + 32x2 + (4x * 3y + 7y * 3y)) = 0 (56xy + 32x2 + (12xy + 21y2)) = 0 Reorder the terms: (56xy + 12xy + 32x2 + 21y2) = 0 Combine like terms: 56xy + 12xy = 68xy (68xy + 32x2 + 21y2) = 0 Solving 68xy + 32x2 + 21y2 = 0 Solving for variable 'x'. Factor a trinomial. (8x + 3y)(4x + 7y) = 0Subproblem 1
Set the factor '(8x + 3y)' equal to zero and attempt to solve: Simplifying 8x + 3y = 0 Solving 8x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 8x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 8x + 0 = 0 + -3y 8x = 0 + -3y Remove the zero: 8x = -3y Divide each side by '8'. x = -0.375y Simplifying x = -0.375ySubproblem 2
Set the factor '(4x + 7y)' equal to zero and attempt to solve: Simplifying 4x + 7y = 0 Solving 4x + 7y = 0 Move all terms containing x to the left, all other terms to the right. Add '-7y' to each side of the equation. 4x + 7y + -7y = 0 + -7y Combine like terms: 7y + -7y = 0 4x + 0 = 0 + -7y 4x = 0 + -7y Remove the zero: 4x = -7y Divide each side by '4'. x = -1.75y Simplifying x = -1.75ySolution
x = {-0.375y, -1.75y}
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