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Simplifying 8(z + -1a)(z + -4) = 0 Reorder the terms: 8(-1a + z)(z + -4) = 0 Reorder the terms: 8(-1a + z)(-4 + z) = 0 Multiply (-1a + z) * (-4 + z) 8(-1a * (-4 + z) + z(-4 + z)) = 0 8((-4 * -1a + z * -1a) + z(-4 + z)) = 0 8((4a + -1az) + z(-4 + z)) = 0 8(4a + -1az + (-4 * z + z * z)) = 0 8(4a + -1az + (-4z + z2)) = 0 8(4a + -1az + -4z + z2) = 0 (4a * 8 + -1az * 8 + -4z * 8 + z2 * 8) = 0 (32a + -8az + -32z + 8z2) = 0 Solving 32a + -8az + -32z + 8z2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '32z' to each side of the equation. 32a + -8az + -32z + 32z + 8z2 = 0 + 32z Combine like terms: -32z + 32z = 0 32a + -8az + 0 + 8z2 = 0 + 32z 32a + -8az + 8z2 = 0 + 32z Remove the zero: 32a + -8az + 8z2 = 32z Add '-8z2' to each side of the equation. 32a + -8az + 8z2 + -8z2 = 32z + -8z2 Combine like terms: 8z2 + -8z2 = 0 32a + -8az + 0 = 32z + -8z2 32a + -8az = 32z + -8z2 Reorder the terms: 32a + -8az + -32z + 8z2 = 32z + -32z + -8z2 + 8z2 Combine like terms: 32z + -32z = 0 32a + -8az + -32z + 8z2 = 0 + -8z2 + 8z2 32a + -8az + -32z + 8z2 = -8z2 + 8z2 Combine like terms: -8z2 + 8z2 = 0 32a + -8az + -32z + 8z2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(4a + -1az + -4z + z2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(4a + -1az + -4z + z2)' equal to zero and attempt to solve: Simplifying 4a + -1az + -4z + z2 = 0 Solving 4a + -1az + -4z + z2 = 0 Move all terms containing a to the left, all other terms to the right. Add '4z' to each side of the equation. 4a + -1az + -4z + 4z + z2 = 0 + 4z Combine like terms: -4z + 4z = 0 4a + -1az + 0 + z2 = 0 + 4z 4a + -1az + z2 = 0 + 4z Remove the zero: 4a + -1az + z2 = 4z Add '-1z2' to each side of the equation. 4a + -1az + z2 + -1z2 = 4z + -1z2 Combine like terms: z2 + -1z2 = 0 4a + -1az + 0 = 4z + -1z2 4a + -1az = 4z + -1z2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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