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Simplifying z2 + 11z + 24 = (z + 8)(z + 3) Reorder the terms: 24 + 11z + z2 = (z + 8)(z + 3) Reorder the terms: 24 + 11z + z2 = (8 + z)(z + 3) Reorder the terms: 24 + 11z + z2 = (8 + z)(3 + z) Multiply (8 + z) * (3 + z) 24 + 11z + z2 = (8(3 + z) + z(3 + z)) 24 + 11z + z2 = ((3 * 8 + z * 8) + z(3 + z)) 24 + 11z + z2 = ((24 + 8z) + z(3 + z)) 24 + 11z + z2 = (24 + 8z + (3 * z + z * z)) 24 + 11z + z2 = (24 + 8z + (3z + z2)) Combine like terms: 8z + 3z = 11z 24 + 11z + z2 = (24 + 11z + z2) Add '-24' to each side of the equation. 24 + 11z + -24 + z2 = 24 + 11z + -24 + z2 Reorder the terms: 24 + -24 + 11z + z2 = 24 + 11z + -24 + z2 Combine like terms: 24 + -24 = 0 0 + 11z + z2 = 24 + 11z + -24 + z2 11z + z2 = 24 + 11z + -24 + z2 Reorder the terms: 11z + z2 = 24 + -24 + 11z + z2 Combine like terms: 24 + -24 = 0 11z + z2 = 0 + 11z + z2 11z + z2 = 11z + z2 Add '-11z' to each side of the equation. 11z + -11z + z2 = 11z + -11z + z2 Combine like terms: 11z + -11z = 0 0 + z2 = 11z + -11z + z2 z2 = 11z + -11z + z2 Combine like terms: 11z + -11z = 0 z2 = 0 + z2 z2 = z2 Add '-1z2' to each side of the equation. z2 + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 0 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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