3(5z-7)2(9z-11)=4(8z-7)-111

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Solution for 3(5z-7)2(9z-11)=4(8z-7)-111 equation: 


Simplifying
3(5z + -7) * 2(9z + -11) = 4(8z + -7) + -111

Reorder the terms:
3(-7 + 5z) * 2(9z + -11) = 4(8z + -7) + -111

Reorder the terms:
3(-7 + 5z) * 2(-11 + 9z) = 4(8z + -7) + -111

Reorder the terms for easier multiplication:
3 * 2(-7 + 5z)(-11 + 9z) = 4(8z + -7) + -111

Multiply 3 * 2
6(-7 + 5z)(-11 + 9z) = 4(8z + -7) + -111

Multiply (-7 + 5z) * (-11 + 9z)
6(-7(-11 + 9z) + 5z * (-11 + 9z)) = 4(8z + -7) + -111
6((-11 * -7 + 9z * -7) + 5z * (-11 + 9z)) = 4(8z + -7) + -111
6((77 + -63z) + 5z * (-11 + 9z)) = 4(8z + -7) + -111
6(77 + -63z + (-11 * 5z + 9z * 5z)) = 4(8z + -7) + -111
6(77 + -63z + (-55z + 45z2)) = 4(8z + -7) + -111

Combine like terms: -63z + -55z = -118z
6(77 + -118z + 45z2) = 4(8z + -7) + -111
(77 * 6 + -118z * 6 + 45z2 * 6) = 4(8z + -7) + -111
(462 + -708z + 270z2) = 4(8z + -7) + -111

Reorder the terms:
462 + -708z + 270z2 = 4(-7 + 8z) + -111
462 + -708z + 270z2 = (-7 * 4 + 8z * 4) + -111
462 + -708z + 270z2 = (-28 + 32z) + -111

Reorder the terms:
462 + -708z + 270z2 = -28 + -111 + 32z

Combine like terms: -28 + -111 = -139
462 + -708z + 270z2 = -139 + 32z

Solving
462 + -708z + 270z2 = -139 + 32z

Solving for variable 'z'.

Reorder the terms:
462 + 139 + -708z + -32z + 270z2 = -139 + 32z + 139 + -32z

Combine like terms: 462 + 139 = 601
601 + -708z + -32z + 270z2 = -139 + 32z + 139 + -32z

Combine like terms: -708z + -32z = -740z
601 + -740z + 270z2 = -139 + 32z + 139 + -32z

Reorder the terms:
601 + -740z + 270z2 = -139 + 139 + 32z + -32z

Combine like terms: -139 + 139 = 0
601 + -740z + 270z2 = 0 + 32z + -32z
601 + -740z + 270z2 = 32z + -32z

Combine like terms: 32z + -32z = 0
601 + -740z + 270z2 = 0

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

Divide each side by '270'.
2.225925926 + -2.740740741z + z2 = 0.0

Move the constant term to the right:

Add '-2.225925926' to each side of the equation.
2.225925926 + -2.740740741z + -2.225925926 + z2 = 0.0 + -2.225925926

Reorder the terms:
2.225925926 + -2.225925926 + -2.740740741z + z2 = 0.0 + -2.225925926

Combine like terms: 2.225925926 + -2.225925926 = 0.000000000
0.000000000 + -2.740740741z + z2 = 0.0 + -2.225925926
-2.740740741z + z2 = 0.0 + -2.225925926

Combine like terms: 0.0 + -2.225925926 = -2.225925926
-2.740740741z + z2 = -2.225925926

The z term is -2.740740741z.  Take half its coefficient (-1.370370371).
Square it (1.877914954) and add it to both sides.

Add '1.877914954' to each side of the equation.
-2.740740741z + 1.877914954 + z2 = -2.225925926 + 1.877914954

Reorder the terms:
1.877914954 + -2.740740741z + z2 = -2.225925926 + 1.877914954

Combine like terms: -2.225925926 + 1.877914954 = -0.348010972
1.877914954 + -2.740740741z + z2 = -0.348010972

Factor a perfect square on the left side:
(z + -1.370370371)(z + -1.370370371) = -0.348010972

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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