(7z+9)(z+7)=47

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Solution for (7z+9)(z+7)=47 equation: 


Simplifying
(7z + 9)(z + 7) = 47

Reorder the terms:
(9 + 7z)(z + 7) = 47

Reorder the terms:
(9 + 7z)(7 + z) = 47

Multiply (9 + 7z) * (7 + z)
(9(7 + z) + 7z * (7 + z)) = 47
((7 * 9 + z * 9) + 7z * (7 + z)) = 47
((63 + 9z) + 7z * (7 + z)) = 47
(63 + 9z + (7 * 7z + z * 7z)) = 47
(63 + 9z + (49z + 7z2)) = 47

Combine like terms: 9z + 49z = 58z
(63 + 58z + 7z2) = 47

Solving
63 + 58z + 7z2 = 47

Solving for variable 'z'.

Reorder the terms:
63 + -47 + 58z + 7z2 = 47 + -47

Combine like terms: 63 + -47 = 16
16 + 58z + 7z2 = 47 + -47

Combine like terms: 47 + -47 = 0
16 + 58z + 7z2 = 0

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


Subproblem 1
Set the factor '(8 + z)' equal to zero and attempt to solve:

Simplifying
8 + z = 0

Solving
8 + z = 0

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

Add '-8' to each side of the equation.
8 + -8 + z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + z = 0 + -8
z = 0 + -8

Combine like terms: 0 + -8 = -8
z = -8

Simplifying
z = -8

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

Simplifying
2 + 7z = 0

Solving
2 + 7z = 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 + 7z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7z = 0 + -2
7z = 0 + -2

Combine like terms: 0 + -2 = -2
7z = -2

Divide each side by '7'.
z = -0.2857142857

Simplifying
z = -0.2857142857
Solution
z = {-8, -0.2857142857}

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