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