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Simplifying 15z2 + 7 = 20z + 7 Reorder the terms: 7 + 15z2 = 20z + 7 Reorder the terms: 7 + 15z2 = 7 + 20z Add '-7' to each side of the equation. 7 + -7 + 15z2 = 7 + -7 + 20z Combine like terms: 7 + -7 = 0 0 + 15z2 = 7 + -7 + 20z 15z2 = 7 + -7 + 20z Combine like terms: 7 + -7 = 0 15z2 = 0 + 20z 15z2 = 20z Solving 15z2 = 20z Solving for variable 'z'. Reorder the terms: -20z + 15z2 = 20z + -20z Combine like terms: 20z + -20z = 0 -20z + 15z2 = 0 Factor out the Greatest Common Factor (GCF), '5z'. 5z(-4 + 3z) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(-4 + 3z)' equal to zero and attempt to solve: Simplifying -4 + 3z = 0 Solving -4 + 3z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 3z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3z = 0 + 4 3z = 0 + 4 Combine like terms: 0 + 4 = 4 3z = 4 Divide each side by '3'. z = 1.333333333 Simplifying z = 1.333333333Solution
z = {0, 1.333333333}
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