(2z+5)(2z+5)-10=159

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Solution for (2z+5)(2z+5)-10=159 equation: 


Simplifying
(2z + 5)(2z + 5) + -10 = 159

Reorder the terms:
(5 + 2z)(2z + 5) + -10 = 159

Reorder the terms:
(5 + 2z)(5 + 2z) + -10 = 159

Multiply (5 + 2z) * (5 + 2z)
(5(5 + 2z) + 2z * (5 + 2z)) + -10 = 159
((5 * 5 + 2z * 5) + 2z * (5 + 2z)) + -10 = 159
((25 + 10z) + 2z * (5 + 2z)) + -10 = 159
(25 + 10z + (5 * 2z + 2z * 2z)) + -10 = 159
(25 + 10z + (10z + 4z2)) + -10 = 159

Combine like terms: 10z + 10z = 20z
(25 + 20z + 4z2) + -10 = 159

Reorder the terms:
25 + -10 + 20z + 4z2 = 159

Combine like terms: 25 + -10 = 15
15 + 20z + 4z2 = 159

Solving
15 + 20z + 4z2 = 159

Solving for variable 'z'.

Reorder the terms:
15 + -159 + 20z + 4z2 = 159 + -159

Combine like terms: 15 + -159 = -144
-144 + 20z + 4z2 = 159 + -159

Combine like terms: 159 + -159 = 0
-144 + 20z + 4z2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-36 + 5z + z2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-9 + -1z)' equal to zero and attempt to solve:

Simplifying
-9 + -1z = 0

Solving
-9 + -1z = 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 + -1z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1z = 0 + 9
-1z = 0 + 9

Combine like terms: 0 + 9 = 9
-1z = 9

Divide each side by '-1'.
z = -9

Simplifying
z = -9

Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {-9, 4}

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