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

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Solution for (2+z)(4z+7)=0 equation: 


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

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

Multiply (2 + z) * (7 + 4z)
(2(7 + 4z) + z(7 + 4z)) = 0
((7 * 2 + 4z * 2) + z(7 + 4z)) = 0
((14 + 8z) + z(7 + 4z)) = 0
(14 + 8z + (7 * z + 4z * z)) = 0
(14 + 8z + (7z + 4z2)) = 0

Combine like terms: 8z + 7z = 15z
(14 + 15z + 4z2) = 0

Solving
14 + 15z + 4z2 = 0

Solving for variable 'z'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(7 + 4z)' equal to zero and attempt to solve:

Simplifying
7 + 4z = 0

Solving
7 + 4z = 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 + 4z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4z = 0 + -7
4z = 0 + -7

Combine like terms: 0 + -7 = -7
4z = -7

Divide each side by '4'.
z = -1.75

Simplifying
z = -1.75
Solution
z = {-2, -1.75}

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