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Simplifying 3z(z + -4) + 8(z + -4) = 0 Reorder the terms: 3z(-4 + z) + 8(z + -4) = 0 (-4 * 3z + z * 3z) + 8(z + -4) = 0 (-12z + 3z2) + 8(z + -4) = 0 Reorder the terms: -12z + 3z2 + 8(-4 + z) = 0 -12z + 3z2 + (-4 * 8 + z * 8) = 0 -12z + 3z2 + (-32 + 8z) = 0 Reorder the terms: -32 + -12z + 8z + 3z2 = 0 Combine like terms: -12z + 8z = -4z -32 + -4z + 3z2 = 0 Solving -32 + -4z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-8 + -3z)(4 + -1z) = 0Subproblem 1
Set the factor '(-8 + -3z)' equal to zero and attempt to solve: Simplifying -8 + -3z = 0 Solving -8 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3z = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3z = 0 + 8 -3z = 0 + 8 Combine like terms: 0 + 8 = 8 -3z = 8 Divide each side by '-3'. z = -2.666666667 Simplifying z = -2.666666667Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 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 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Solution
z = {-2.666666667, 4}
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