4(z+9)(-z+3)=0

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Solution for 4(z+9)(-z+3)=0 equation:


Simplifying
4(z + 9)(-1z + 3) = 0

Reorder the terms:
4(9 + z)(-1z + 3) = 0

Reorder the terms:
4(9 + z)(3 + -1z) = 0

Multiply (9 + z) * (3 + -1z)
4(9(3 + -1z) + z(3 + -1z)) = 0
4((3 * 9 + -1z * 9) + z(3 + -1z)) = 0
4((27 + -9z) + z(3 + -1z)) = 0
4(27 + -9z + (3 * z + -1z * z)) = 0
4(27 + -9z + (3z + -1z2)) = 0

Combine like terms: -9z + 3z = -6z
4(27 + -6z + -1z2) = 0
(27 * 4 + -6z * 4 + -1z2 * 4) = 0
(108 + -24z + -4z2) = 0

Solving
108 + -24z + -4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(27 + -6z + -1z2) = 0

Factor a trinomial.
4((3 + -1z)(9 + z)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3

Subproblem 2

Set the factor '(9 + z)' equal to zero and attempt to solve: Simplifying 9 + z = 0 Solving 9 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + z = 0 + -9 z = 0 + -9 Combine like terms: 0 + -9 = -9 z = -9 Simplifying z = -9

Solution

z = {3, -9}

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