-4(z^2+10z+25)=-676

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Solution for -4(z^2+10z+25)=-676 equation: 


Simplifying
-4(z2 + 10z + 25) = -676

Reorder the terms:
-4(25 + 10z + z2) = -676
(25 * -4 + 10z * -4 + z2 * -4) = -676
(-100 + -40z + -4z2) = -676

Solving
-100 + -40z + -4z2 = -676

Solving for variable 'z'.

Reorder the terms:
-100 + 676 + -40z + -4z2 = -676 + 676

Combine like terms: -100 + 676 = 576
576 + -40z + -4z2 = -676 + 676

Combine like terms: -676 + 676 = 0
576 + -40z + -4z2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(144 + -10z + -1z2) = 0

Factor a trinomial.
4((8 + -1z)(18 + z)) = 0

Ignore the factor 4.

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

Simplifying
8 + -1z = 0

Solving
8 + -1z = 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 + -1z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1z = 0 + -8
-1z = 0 + -8

Combine like terms: 0 + -8 = -8
-1z = -8

Divide each side by '-1'.
z = 8

Simplifying
z = 8

Subproblem 2
Set the factor '(18 + z)' equal to zero and attempt to solve:

Simplifying
18 + z = 0

Solving
18 + z = 0

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

Add '-18' to each side of the equation.
18 + -18 + z = 0 + -18

Combine like terms: 18 + -18 = 0
0 + z = 0 + -18
z = 0 + -18

Combine like terms: 0 + -18 = -18
z = -18

Simplifying
z = -18
Solution
z = {8, -18}

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