(3z+6)(4z+9)=

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Solution for (3z+6)(4z+9)= equation:


Simplifying
(3z + 6)(4z + 9) = 0

Reorder the terms:
(6 + 3z)(4z + 9) = 0

Reorder the terms:
(6 + 3z)(9 + 4z) = 0

Multiply (6 + 3z) * (9 + 4z)
(6(9 + 4z) + 3z * (9 + 4z)) = 0
((9 * 6 + 4z * 6) + 3z * (9 + 4z)) = 0
((54 + 24z) + 3z * (9 + 4z)) = 0
(54 + 24z + (9 * 3z + 4z * 3z)) = 0
(54 + 24z + (27z + 12z2)) = 0

Combine like terms: 24z + 27z = 51z
(54 + 51z + 12z2) = 0

Solving
54 + 51z + 12z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + 17z + 4z2) = 0

Factor a trinomial.
3((9 + 4z)(2 + z)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(9 + 4z)' equal to zero and attempt to solve: Simplifying 9 + 4z = 0 Solving 9 + 4z = 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 + 4z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4z = 0 + -9 4z = 0 + -9 Combine like terms: 0 + -9 = -9 4z = -9 Divide each side by '4'. z = -2.25 Simplifying z = -2.25

Subproblem 2

Set the factor '(2 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 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 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2

Solution

z = {-2.25, -2}

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