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Simplifying 25z2 + -9z4 = 0 Solving 25z2 + -9z4 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z2'. z2(25 + -9z2) = 0 Factor a difference between two squares. z2((5 + 3z)(5 + -3z)) = 0Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve: Simplifying z2 = 0 Solving z2 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z2 = 0 Take the square root of each side: z = {0}Subproblem 2
Set the factor '(5 + 3z)' equal to zero and attempt to solve: Simplifying 5 + 3z = 0 Solving 5 + 3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3z = 0 + -5 3z = 0 + -5 Combine like terms: 0 + -5 = -5 3z = -5 Divide each side by '3'. z = -1.666666667 Simplifying z = -1.666666667Subproblem 3
Set the factor '(5 + -3z)' equal to zero and attempt to solve: Simplifying 5 + -3z = 0 Solving 5 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3z = 0 + -5 -3z = 0 + -5 Combine like terms: 0 + -5 = -5 -3z = -5 Divide each side by '-3'. z = 1.666666667 Simplifying z = 1.666666667Solution
z = {0, -1.666666667, 1.666666667}
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