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Simplifying 4(8 + -3y) = 32 + -8(y + 2) * fory (8 * 4 + -3y * 4) = 32 + -8(y + 2) * fory (32 + -12y) = 32 + -8(y + 2) * fory Reorder the terms: 32 + -12y = 32 + -8(2 + y) * fory Reorder the terms for easier multiplication: 32 + -12y = 32 + -8fory(2 + y) 32 + -12y = 32 + (2 * -8fory + y * -8fory) 32 + -12y = 32 + (-16fory + -8fory2) Add '-32' to each side of the equation. 32 + -32 + -12y = 32 + -16fory + -32 + -8fory2 Combine like terms: 32 + -32 = 0 0 + -12y = 32 + -16fory + -32 + -8fory2 -12y = 32 + -16fory + -32 + -8fory2 Reorder the terms: -12y = 32 + -32 + -16fory + -8fory2 Combine like terms: 32 + -32 = 0 -12y = 0 + -16fory + -8fory2 -12y = -16fory + -8fory2 Solving -12y = -16fory + -8fory2 Solving for variable 'y'. Reorder the terms: 16fory + 8fory2 + -12y = -16fory + -8fory2 + 16fory + 8fory2 Reorder the terms: 16fory + 8fory2 + -12y = -16fory + 16fory + -8fory2 + 8fory2 Combine like terms: -16fory + 16fory = 0 16fory + 8fory2 + -12y = 0 + -8fory2 + 8fory2 16fory + 8fory2 + -12y = -8fory2 + 8fory2 Combine like terms: -8fory2 + 8fory2 = 0 16fory + 8fory2 + -12y = 0 Factor out the Greatest Common Factor (GCF), '4y'. 4y(4for + 2fory + -3) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(4for + 2fory + -3)' equal to zero and attempt to solve: Simplifying 4for + 2fory + -3 = 0 Reorder the terms: -3 + 4for + 2fory = 0 Solving -3 + 4for + 2fory = 0 Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 4for + 3 + 2fory = 0 + 3 Reorder the terms: -3 + 3 + 4for + 2fory = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4for + 2fory = 0 + 3 4for + 2fory = 0 + 3 Combine like terms: 0 + 3 = 3 4for + 2fory = 3 Add '-4for' to each side of the equation. 4for + -4for + 2fory = 3 + -4for Combine like terms: 4for + -4for = 0 0 + 2fory = 3 + -4for 2fory = 3 + -4for Divide each side by '2for'. y = 1.5f-1o-1r-1 + -2 Simplifying y = 1.5f-1o-1r-1 + -2 Reorder the terms: y = -2 + 1.5f-1o-1r-1Solution
y = {0, -2 + 1.5f-1o-1r-1}
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