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Simplifying (-7y2 + 3) * 4y2 + 3y2(5y2 + -8) + -1(-7y4 + 3y2) * 2 = 0 Reorder the terms: (3 + -7y2) * 4y2 + 3y2(5y2 + -8) + -1(-7y4 + 3y2) * 2 = 0 Reorder the terms for easier multiplication: 4y2(3 + -7y2) + 3y2(5y2 + -8) + -1(-7y4 + 3y2) * 2 = 0 (3 * 4y2 + -7y2 * 4y2) + 3y2(5y2 + -8) + -1(-7y4 + 3y2) * 2 = 0 (12y2 + -28y4) + 3y2(5y2 + -8) + -1(-7y4 + 3y2) * 2 = 0 Reorder the terms: 12y2 + -28y4 + 3y2(-8 + 5y2) + -1(-7y4 + 3y2) * 2 = 0 12y2 + -28y4 + (-8 * 3y2 + 5y2 * 3y2) + -1(-7y4 + 3y2) * 2 = 0 12y2 + -28y4 + (-24y2 + 15y4) + -1(-7y4 + 3y2) * 2 = 0 Reorder the terms: 12y2 + -28y4 + -24y2 + 15y4 + -1(3y2 + -7y4) * 2 = 0 Reorder the terms for easier multiplication: 12y2 + -28y4 + -24y2 + 15y4 + -1 * 2(3y2 + -7y4) = 0 Multiply -1 * 2 12y2 + -28y4 + -24y2 + 15y4 + -2(3y2 + -7y4) = 0 12y2 + -28y4 + -24y2 + 15y4 + (3y2 * -2 + -7y4 * -2) = 0 12y2 + -28y4 + -24y2 + 15y4 + (-6y2 + 14y4) = 0 Reorder the terms: 12y2 + -24y2 + -6y2 + -28y4 + 15y4 + 14y4 = 0 Combine like terms: 12y2 + -24y2 = -12y2 -12y2 + -6y2 + -28y4 + 15y4 + 14y4 = 0 Combine like terms: -12y2 + -6y2 = -18y2 -18y2 + -28y4 + 15y4 + 14y4 = 0 Combine like terms: -28y4 + 15y4 = -13y4 -18y2 + -13y4 + 14y4 = 0 Combine like terms: -13y4 + 14y4 = 1y4 -18y2 + 1y4 = 0 Solving -18y2 + 1y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y2'. y2(-18 + y2) = 0Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(-18 + y2)' equal to zero and attempt to solve: Simplifying -18 + y2 = 0 Solving -18 + y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + y2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + y2 = 0 + 18 y2 = 0 + 18 Combine like terms: 0 + 18 = 18 y2 = 18 Simplifying y2 = 18 Take the square root of each side: y = {-4.242640687, 4.242640687}Solution
y = {0, -4.242640687, 4.242640687}
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