5(2z-3)(5-z)+4(2z-11)(5-z)=-3(2z-11)(2z-3)

Solution for 5(2z-3)(5-z)+4(2z-11)(5-z)=-3(2z-11)(2z-3) equation:

Simplifying
5(2z + -3)(5 + -1z) + 4(2z + -11)(5 + -1z) = -3(2z + -11)(2z + -3)

Reorder the terms:
5(-3 + 2z)(5 + -1z) + 4(2z + -11)(5 + -1z) = -3(2z + -11)(2z + -3)

Multiply (-3 + 2z) * (5 + -1z)
5(-3(5 + -1z) + 2z * (5 + -1z)) + 4(2z + -11)(5 + -1z) = -3(2z + -11)(2z + -3)
5((5 * -3 + -1z * -3) + 2z * (5 + -1z)) + 4(2z + -11)(5 + -1z) = -3(2z + -11)(2z + -3)
5((-15 + 3z) + 2z * (5 + -1z)) + 4(2z + -11)(5 + -1z) = -3(2z + -11)(2z + -3)
5(-15 + 3z + (5 * 2z + -1z * 2z)) + 4(2z + -11)(5 + -1z) = -3(2z + -11)(2z + -3)
5(-15 + 3z + (10z + -2z2)) + 4(2z + -11)(5 + -1z) = -3(2z + -11)(2z + -3)

Combine like terms: 3z + 10z = 13z
5(-15 + 13z + -2z2) + 4(2z + -11)(5 + -1z) = -3(2z + -11)(2z + -3)
(-15 * 5 + 13z * 5 + -2z2 * 5) + 4(2z + -11)(5 + -1z) = -3(2z + -11)(2z + -3)
(-75 + 65z + -10z2) + 4(2z + -11)(5 + -1z) = -3(2z + -11)(2z + -3)

Reorder the terms:
-75 + 65z + -10z2 + 4(-11 + 2z)(5 + -1z) = -3(2z + -11)(2z + -3)

Multiply (-11 + 2z) * (5 + -1z)
-75 + 65z + -10z2 + 4(-11(5 + -1z) + 2z * (5 + -1z)) = -3(2z + -11)(2z + -3)
-75 + 65z + -10z2 + 4((5 * -11 + -1z * -11) + 2z * (5 + -1z)) = -3(2z + -11)(2z + -3)
-75 + 65z + -10z2 + 4((-55 + 11z) + 2z * (5 + -1z)) = -3(2z + -11)(2z + -3)
-75 + 65z + -10z2 + 4(-55 + 11z + (5 * 2z + -1z * 2z)) = -3(2z + -11)(2z + -3)
-75 + 65z + -10z2 + 4(-55 + 11z + (10z + -2z2)) = -3(2z + -11)(2z + -3)

Combine like terms: 11z + 10z = 21z
-75 + 65z + -10z2 + 4(-55 + 21z + -2z2) = -3(2z + -11)(2z + -3)
-75 + 65z + -10z2 + (-55 * 4 + 21z * 4 + -2z2 * 4) = -3(2z + -11)(2z + -3)
-75 + 65z + -10z2 + (-220 + 84z + -8z2) = -3(2z + -11)(2z + -3)

Reorder the terms:
-75 + -220 + 65z + 84z + -10z2 + -8z2 = -3(2z + -11)(2z + -3)

Combine like terms: -75 + -220 = -295
-295 + 65z + 84z + -10z2 + -8z2 = -3(2z + -11)(2z + -3)

Combine like terms: 65z + 84z = 149z
-295 + 149z + -10z2 + -8z2 = -3(2z + -11)(2z + -3)

Combine like terms: -10z2 + -8z2 = -18z2
-295 + 149z + -18z2 = -3(2z + -11)(2z + -3)

Reorder the terms:
-295 + 149z + -18z2 = -3(-11 + 2z)(2z + -3)

Reorder the terms:
-295 + 149z + -18z2 = -3(-11 + 2z)(-3 + 2z)

Multiply (-11 + 2z) * (-3 + 2z)
-295 + 149z + -18z2 = -3(-11(-3 + 2z) + 2z * (-3 + 2z))
-295 + 149z + -18z2 = -3((-3 * -11 + 2z * -11) + 2z * (-3 + 2z))
-295 + 149z + -18z2 = -3((33 + -22z) + 2z * (-3 + 2z))
-295 + 149z + -18z2 = -3(33 + -22z + (-3 * 2z + 2z * 2z))
-295 + 149z + -18z2 = -3(33 + -22z + (-6z + 4z2))

Combine like terms: -22z + -6z = -28z
-295 + 149z + -18z2 = -3(33 + -28z + 4z2)
-295 + 149z + -18z2 = (33 * -3 + -28z * -3 + 4z2 * -3)
-295 + 149z + -18z2 = (-99 + 84z + -12z2)

Solving
-295 + 149z + -18z2 = -99 + 84z + -12z2

Solving for variable 'z'.

Reorder the terms:
-295 + 99 + 149z + -84z + -18z2 + 12z2 = -99 + 84z + -12z2 + 99 + -84z + 12z2

Combine like terms: -295 + 99 = -196
-196 + 149z + -84z + -18z2 + 12z2 = -99 + 84z + -12z2 + 99 + -84z + 12z2

Combine like terms: 149z + -84z = 65z
-196 + 65z + -18z2 + 12z2 = -99 + 84z + -12z2 + 99 + -84z + 12z2

Combine like terms: -18z2 + 12z2 = -6z2
-196 + 65z + -6z2 = -99 + 84z + -12z2 + 99 + -84z + 12z2

Reorder the terms:
-196 + 65z + -6z2 = -99 + 99 + 84z + -84z + -12z2 + 12z2

Combine like terms: -99 + 99 = 0
-196 + 65z + -6z2 = 0 + 84z + -84z + -12z2 + 12z2
-196 + 65z + -6z2 = 84z + -84z + -12z2 + 12z2

Combine like terms: 84z + -84z = 0
-196 + 65z + -6z2 = 0 + -12z2 + 12z2
-196 + 65z + -6z2 = -12z2 + 12z2

Combine like terms: -12z2 + 12z2 = 0
-196 + 65z + -6z2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
32.66666667 + -10.83333333z + z2 = 0

Move the constant term to the right:

Add '-32.66666667' to each side of the equation.
32.66666667 + -10.83333333z + -32.66666667 + z2 = 0 + -32.66666667

Reorder the terms:
32.66666667 + -32.66666667 + -10.83333333z + z2 = 0 + -32.66666667

Combine like terms: 32.66666667 + -32.66666667 = 0.00000000
0.00000000 + -10.83333333z + z2 = 0 + -32.66666667
-10.83333333z + z2 = 0 + -32.66666667

Combine like terms: 0 + -32.66666667 = -32.66666667
-10.83333333z + z2 = -32.66666667

The z term is -10.83333333z.  Take half its coefficient (-5.416666665).
Square it (29.34027776) and add it to both sides.

Add '29.34027776' to each side of the equation.
-10.83333333z + 29.34027776 + z2 = -32.66666667 + 29.34027776

Reorder the terms:
29.34027776 + -10.83333333z + z2 = -32.66666667 + 29.34027776

Combine like terms: -32.66666667 + 29.34027776 = -3.32638891
29.34027776 + -10.83333333z + z2 = -3.32638891

Factor a perfect square on the left side:
(z + -5.416666665)(z + -5.416666665) = -3.32638891

Can't calculate square root of the right side.

The solution to this equation could not be determined.