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Simplifying (2z + -3)(z + 4) = (3z + -2)(z + 6) Reorder the terms: (-3 + 2z)(z + 4) = (3z + -2)(z + 6) Reorder the terms: (-3 + 2z)(4 + z) = (3z + -2)(z + 6) Multiply (-3 + 2z) * (4 + z) (-3(4 + z) + 2z * (4 + z)) = (3z + -2)(z + 6) ((4 * -3 + z * -3) + 2z * (4 + z)) = (3z + -2)(z + 6) ((-12 + -3z) + 2z * (4 + z)) = (3z + -2)(z + 6) (-12 + -3z + (4 * 2z + z * 2z)) = (3z + -2)(z + 6) (-12 + -3z + (8z + 2z2)) = (3z + -2)(z + 6) Combine like terms: -3z + 8z = 5z (-12 + 5z + 2z2) = (3z + -2)(z + 6) Reorder the terms: -12 + 5z + 2z2 = (-2 + 3z)(z + 6) Reorder the terms: -12 + 5z + 2z2 = (-2 + 3z)(6 + z) Multiply (-2 + 3z) * (6 + z) -12 + 5z + 2z2 = (-2(6 + z) + 3z * (6 + z)) -12 + 5z + 2z2 = ((6 * -2 + z * -2) + 3z * (6 + z)) -12 + 5z + 2z2 = ((-12 + -2z) + 3z * (6 + z)) -12 + 5z + 2z2 = (-12 + -2z + (6 * 3z + z * 3z)) -12 + 5z + 2z2 = (-12 + -2z + (18z + 3z2)) Combine like terms: -2z + 18z = 16z -12 + 5z + 2z2 = (-12 + 16z + 3z2) Add '12' to each side of the equation. -12 + 5z + 12 + 2z2 = -12 + 16z + 12 + 3z2 Reorder the terms: -12 + 12 + 5z + 2z2 = -12 + 16z + 12 + 3z2 Combine like terms: -12 + 12 = 0 0 + 5z + 2z2 = -12 + 16z + 12 + 3z2 5z + 2z2 = -12 + 16z + 12 + 3z2 Reorder the terms: 5z + 2z2 = -12 + 12 + 16z + 3z2 Combine like terms: -12 + 12 = 0 5z + 2z2 = 0 + 16z + 3z2 5z + 2z2 = 16z + 3z2 Solving 5z + 2z2 = 16z + 3z2 Solving for variable 'z'. Reorder the terms: 5z + -16z + 2z2 + -3z2 = 16z + 3z2 + -16z + -3z2 Combine like terms: 5z + -16z = -11z -11z + 2z2 + -3z2 = 16z + 3z2 + -16z + -3z2 Combine like terms: 2z2 + -3z2 = -1z2 -11z + -1z2 = 16z + 3z2 + -16z + -3z2 Reorder the terms: -11z + -1z2 = 16z + -16z + 3z2 + -3z2 Combine like terms: 16z + -16z = 0 -11z + -1z2 = 0 + 3z2 + -3z2 -11z + -1z2 = 3z2 + -3z2 Combine like terms: 3z2 + -3z2 = 0 -11z + -1z2 = 0 Factor out the Greatest Common Factor (GCF), '-1z'. -1z(11 + z) = 0 Ignore the factor -1.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 '(11 + z)' equal to zero and attempt to solve: Simplifying 11 + z = 0 Solving 11 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + z = 0 + -11 Combine like terms: 11 + -11 = 0 0 + z = 0 + -11 z = 0 + -11 Combine like terms: 0 + -11 = -11 z = -11 Simplifying z = -11Solution
z = {0, -11}
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