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Simplifying (5z2 + -4z)(z + 3) = 0 Reorder the terms: (-4z + 5z2)(z + 3) = 0 Reorder the terms: (-4z + 5z2)(3 + z) = 0 Multiply (-4z + 5z2) * (3 + z) (-4z * (3 + z) + 5z2 * (3 + z)) = 0 ((3 * -4z + z * -4z) + 5z2 * (3 + z)) = 0 ((-12z + -4z2) + 5z2 * (3 + z)) = 0 (-12z + -4z2 + (3 * 5z2 + z * 5z2)) = 0 (-12z + -4z2 + (15z2 + 5z3)) = 0 Combine like terms: -4z2 + 15z2 = 11z2 (-12z + 11z2 + 5z3) = 0 Solving -12z + 11z2 + 5z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-12 + 11z + 5z2) = 0 Factor a trinomial. z((-3 + -1z)(4 + -5z)) = 0Subproblem 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 + -1z)' equal to zero and attempt to solve: Simplifying -3 + -1z = 0 Solving -3 + -1z = 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 + -1z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1z = 0 + 3 -1z = 0 + 3 Combine like terms: 0 + 3 = 3 -1z = 3 Divide each side by '-1'. z = -3 Simplifying z = -3Subproblem 3
Set the factor '(4 + -5z)' equal to zero and attempt to solve: Simplifying 4 + -5z = 0 Solving 4 + -5z = 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 + -5z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5z = 0 + -4 -5z = 0 + -4 Combine like terms: 0 + -4 = -4 -5z = -4 Divide each side by '-5'. z = 0.8 Simplifying z = 0.8Solution
z = {0, -3, 0.8}
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