-2.7z(z+1.5)=1.8(z+4)

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Solution for -2.7z(z+1.5)=1.8(z+4) equation: 


Simplifying
-2.7z(z + 1.5) = 1.8(z + 4)

Reorder the terms:
-2.7z(1.5 + z) = 1.8(z + 4)
(1.5 * -2.7z + z * -2.7z) = 1.8(z + 4)
(-4.05z + -2.7z2) = 1.8(z + 4)

Reorder the terms:
-4.05z + -2.7z2 = 1.8(4 + z)
-4.05z + -2.7z2 = (4 * 1.8 + z * 1.8)
-4.05z + -2.7z2 = (7.2 + 1.8z)

Solving
-4.05z + -2.7z2 = 7.2 + 1.8z

Solving for variable 'z'.

Reorder the terms:
-7.2 + -4.05z + -1.8z + -2.7z2 = 7.2 + 1.8z + -7.2 + -1.8z

Combine like terms: -4.05z + -1.8z = -5.85z
-7.2 + -5.85z + -2.7z2 = 7.2 + 1.8z + -7.2 + -1.8z

Reorder the terms:
-7.2 + -5.85z + -2.7z2 = 7.2 + -7.2 + 1.8z + -1.8z

Combine like terms: 7.2 + -7.2 = 0.0
-7.2 + -5.85z + -2.7z2 = 0.0 + 1.8z + -1.8z
-7.2 + -5.85z + -2.7z2 = 1.8z + -1.8z

Combine like terms: 1.8z + -1.8z = 0.0
-7.2 + -5.85z + -2.7z2 = 0.0

Begin completing the square.  Divide all terms by
-2.7 the coefficient of the squared term: 

Divide each side by '-2.7'.
2.666666667 + 2.166666667z + z2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + 2.166666667z + -2.666666667 + z2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + 2.166666667z + z2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + 2.166666667z + z2 = 0 + -2.666666667
2.166666667z + z2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
2.166666667z + z2 = -2.666666667

The z term is 2.166666667z.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667z + 1.173611113 + z2 = -2.666666667 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667z + z2 = -2.666666667 + 1.173611113

Combine like terms: -2.666666667 + 1.173611113 = -1.493055554
1.173611113 + 2.166666667z + z2 = -1.493055554

Factor a perfect square on the left side:
(z + 1.083333334)(z + 1.083333334) = -1.493055554

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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