(7+z)(4z+9)=0

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Solution for (7+z)(4z+9)=0 equation: 


Simplifying
(7 + z)(4z + 9) = 0

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

Multiply (7 + z) * (9 + 4z)
(7(9 + 4z) + z(9 + 4z)) = 0
((9 * 7 + 4z * 7) + z(9 + 4z)) = 0
((63 + 28z) + z(9 + 4z)) = 0
(63 + 28z + (9 * z + 4z * z)) = 0
(63 + 28z + (9z + 4z2)) = 0

Combine like terms: 28z + 9z = 37z
(63 + 37z + 4z2) = 0

Solving
63 + 37z + 4z2 = 0

Solving for variable 'z'.

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


Subproblem 1
Set the factor '(7 + z)' equal to zero and attempt to solve:

Simplifying
7 + z = 0

Solving
7 + z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + z = 0 + -7
z = 0 + -7

Combine like terms: 0 + -7 = -7
z = -7

Simplifying
z = -7

Subproblem 2
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
Solution
z = {-7, -2.25}

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