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Simplifying (8z + -2)(5z + 4) = (4z + -1)(8z + 8) Reorder the terms: (-2 + 8z)(5z + 4) = (4z + -1)(8z + 8) Reorder the terms: (-2 + 8z)(4 + 5z) = (4z + -1)(8z + 8) Multiply (-2 + 8z) * (4 + 5z) (-2(4 + 5z) + 8z * (4 + 5z)) = (4z + -1)(8z + 8) ((4 * -2 + 5z * -2) + 8z * (4 + 5z)) = (4z + -1)(8z + 8) ((-8 + -10z) + 8z * (4 + 5z)) = (4z + -1)(8z + 8) (-8 + -10z + (4 * 8z + 5z * 8z)) = (4z + -1)(8z + 8) (-8 + -10z + (32z + 40z2)) = (4z + -1)(8z + 8) Combine like terms: -10z + 32z = 22z (-8 + 22z + 40z2) = (4z + -1)(8z + 8) Reorder the terms: -8 + 22z + 40z2 = (-1 + 4z)(8z + 8) Reorder the terms: -8 + 22z + 40z2 = (-1 + 4z)(8 + 8z) Multiply (-1 + 4z) * (8 + 8z) -8 + 22z + 40z2 = (-1(8 + 8z) + 4z * (8 + 8z)) -8 + 22z + 40z2 = ((8 * -1 + 8z * -1) + 4z * (8 + 8z)) -8 + 22z + 40z2 = ((-8 + -8z) + 4z * (8 + 8z)) -8 + 22z + 40z2 = (-8 + -8z + (8 * 4z + 8z * 4z)) -8 + 22z + 40z2 = (-8 + -8z + (32z + 32z2)) Combine like terms: -8z + 32z = 24z -8 + 22z + 40z2 = (-8 + 24z + 32z2) Add '8' to each side of the equation. -8 + 22z + 8 + 40z2 = -8 + 24z + 8 + 32z2 Reorder the terms: -8 + 8 + 22z + 40z2 = -8 + 24z + 8 + 32z2 Combine like terms: -8 + 8 = 0 0 + 22z + 40z2 = -8 + 24z + 8 + 32z2 22z + 40z2 = -8 + 24z + 8 + 32z2 Reorder the terms: 22z + 40z2 = -8 + 8 + 24z + 32z2 Combine like terms: -8 + 8 = 0 22z + 40z2 = 0 + 24z + 32z2 22z + 40z2 = 24z + 32z2 Solving 22z + 40z2 = 24z + 32z2 Solving for variable 'z'. Reorder the terms: 22z + -24z + 40z2 + -32z2 = 24z + 32z2 + -24z + -32z2 Combine like terms: 22z + -24z = -2z -2z + 40z2 + -32z2 = 24z + 32z2 + -24z + -32z2 Combine like terms: 40z2 + -32z2 = 8z2 -2z + 8z2 = 24z + 32z2 + -24z + -32z2 Reorder the terms: -2z + 8z2 = 24z + -24z + 32z2 + -32z2 Combine like terms: 24z + -24z = 0 -2z + 8z2 = 0 + 32z2 + -32z2 -2z + 8z2 = 32z2 + -32z2 Combine like terms: 32z2 + -32z2 = 0 -2z + 8z2 = 0 Factor out the Greatest Common Factor (GCF), '2z'. 2z(-1 + 4z) = 0 Ignore the factor 2.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 '(-1 + 4z)' equal to zero and attempt to solve: Simplifying -1 + 4z = 0 Solving -1 + 4z = 0 Move all terms containing z to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 4z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4z = 0 + 1 4z = 0 + 1 Combine like terms: 0 + 1 = 1 4z = 1 Divide each side by '4'. z = 0.25 Simplifying z = 0.25Solution
z = {0, 0.25}
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