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Simplifying -6(-4z + 6z2) + 3(4z + -4z2) = 0 (-4z * -6 + 6z2 * -6) + 3(4z + -4z2) = 0 (24z + -36z2) + 3(4z + -4z2) = 0 24z + -36z2 + (4z * 3 + -4z2 * 3) = 0 24z + -36z2 + (12z + -12z2) = 0 Reorder the terms: 24z + 12z + -36z2 + -12z2 = 0 Combine like terms: 24z + 12z = 36z 36z + -36z2 + -12z2 = 0 Combine like terms: -36z2 + -12z2 = -48z2 36z + -48z2 = 0 Solving 36z + -48z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '12z'. 12z(3 + -4z) = 0 Ignore the factor 12.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 '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75Solution
z = {0, 0.75}
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