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Simplifying 90 + -5r + -0.9(30 + 0.5y) * y + 177 + 225 + -60r + (50 + -55 + 0.105y) = 0 Reorder the terms for easier multiplication: 90 + -5r + -0.9y(30 + 0.5y) + 177 + 225 + -60r + (50 + -55 + 0.105y) = 0 90 + -5r + (30 * -0.9y + 0.5y * -0.9y) + 177 + 225 + -60r + (50 + -55 + 0.105y) = 0 90 + -5r + (-27y + -0.45y2) + 177 + 225 + -60r + (50 + -55 + 0.105y) = 0 Combine like terms: 50 + -55 = -5 90 + -5r + -27y + -0.45y2 + 177 + 225 + -60r + (-5 + 0.105y) = 0 Remove parenthesis around (-5 + 0.105y) 90 + -5r + -27y + -0.45y2 + 177 + 225 + -60r + -5 + 0.105y = 0 Reorder the terms: 90 + 177 + 225 + -5 + -5r + -60r + -27y + 0.105y + -0.45y2 = 0 Combine like terms: 90 + 177 = 267 267 + 225 + -5 + -5r + -60r + -27y + 0.105y + -0.45y2 = 0 Combine like terms: 267 + 225 = 492 492 + -5 + -5r + -60r + -27y + 0.105y + -0.45y2 = 0 Combine like terms: 492 + -5 = 487 487 + -5r + -60r + -27y + 0.105y + -0.45y2 = 0 Combine like terms: -5r + -60r = -65r 487 + -65r + -27y + 0.105y + -0.45y2 = 0 Combine like terms: -27y + 0.105y = -26.895y 487 + -65r + -26.895y + -0.45y2 = 0 Solving 487 + -65r + -26.895y + -0.45y2 = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-487' to each side of the equation. 487 + -65r + -26.895y + -487 + -0.45y2 = 0 + -487 Reorder the terms: 487 + -487 + -65r + -26.895y + -0.45y2 = 0 + -487 Combine like terms: 487 + -487 = 0 0 + -65r + -26.895y + -0.45y2 = 0 + -487 -65r + -26.895y + -0.45y2 = 0 + -487 Combine like terms: 0 + -487 = -487 -65r + -26.895y + -0.45y2 = -487 Add '26.895y' to each side of the equation. -65r + -26.895y + 26.895y + -0.45y2 = -487 + 26.895y Combine like terms: -26.895y + 26.895y = 0.000 -65r + 0.000 + -0.45y2 = -487 + 26.895y -65r + -0.45y2 = -487 + 26.895y Add '0.45y2' to each side of the equation. -65r + -0.45y2 + 0.45y2 = -487 + 26.895y + 0.45y2 Combine like terms: -0.45y2 + 0.45y2 = 0.00 -65r + 0.00 = -487 + 26.895y + 0.45y2 -65r = -487 + 26.895y + 0.45y2 Divide each side by '-65'. r = 7.492307692 + -0.4137692308y + -0.006923076923y2 Simplifying r = 7.492307692 + -0.4137692308y + -0.006923076923y2
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