(4z^2+9z-12)-(5z^2-z+3)=4z^2+9z-12

Solution for (4z^2+9z-12)-(5z^2-z+3)=4z^2+9z-12 equation:

Simplifying
(4z2 + 9z + -12) + -1(5z2 + -1z + 3) = 4z2 + 9z + -12

Reorder the terms:
(-12 + 9z + 4z2) + -1(5z2 + -1z + 3) = 4z2 + 9z + -12

Remove parenthesis around (-12 + 9z + 4z2)
-12 + 9z + 4z2 + -1(5z2 + -1z + 3) = 4z2 + 9z + -12

Reorder the terms:
-12 + 9z + 4z2 + -1(3 + -1z + 5z2) = 4z2 + 9z + -12
-12 + 9z + 4z2 + (3 * -1 + -1z * -1 + 5z2 * -1) = 4z2 + 9z + -12
-12 + 9z + 4z2 + (-3 + 1z + -5z2) = 4z2 + 9z + -12

Reorder the terms:
-12 + -3 + 9z + 1z + 4z2 + -5z2 = 4z2 + 9z + -12

Combine like terms: -12 + -3 = -15
-15 + 9z + 1z + 4z2 + -5z2 = 4z2 + 9z + -12

Combine like terms: 9z + 1z = 10z
-15 + 10z + 4z2 + -5z2 = 4z2 + 9z + -12

Combine like terms: 4z2 + -5z2 = -1z2
-15 + 10z + -1z2 = 4z2 + 9z + -12

Reorder the terms:
-15 + 10z + -1z2 = -12 + 9z + 4z2

Solving
-15 + 10z + -1z2 = -12 + 9z + 4z2

Solving for variable 'z'.

Reorder the terms:
-15 + 12 + 10z + -9z + -1z2 + -4z2 = -12 + 9z + 4z2 + 12 + -9z + -4z2

Combine like terms: -15 + 12 = -3
-3 + 10z + -9z + -1z2 + -4z2 = -12 + 9z + 4z2 + 12 + -9z + -4z2

Combine like terms: 10z + -9z = 1z
-3 + 1z + -1z2 + -4z2 = -12 + 9z + 4z2 + 12 + -9z + -4z2

Combine like terms: -1z2 + -4z2 = -5z2
-3 + 1z + -5z2 = -12 + 9z + 4z2 + 12 + -9z + -4z2

Reorder the terms:
-3 + 1z + -5z2 = -12 + 12 + 9z + -9z + 4z2 + -4z2

Combine like terms: -12 + 12 = 0
-3 + 1z + -5z2 = 0 + 9z + -9z + 4z2 + -4z2
-3 + 1z + -5z2 = 9z + -9z + 4z2 + -4z2

Combine like terms: 9z + -9z = 0
-3 + 1z + -5z2 = 0 + 4z2 + -4z2
-3 + 1z + -5z2 = 4z2 + -4z2

Combine like terms: 4z2 + -4z2 = 0
-3 + 1z + -5z2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.6 + -0.2z + z2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -0.2z + -0.6 + z2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -0.2z + z2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -0.2z + z2 = 0 + -0.6
-0.2z + z2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-0.2z + z2 = -0.6

The z term is -0.2z.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2z + 0.01 + z2 = -0.6 + 0.01

Reorder the terms:
0.01 + -0.2z + z2 = -0.6 + 0.01

Combine like terms: -0.6 + 0.01 = -0.59
0.01 + -0.2z + z2 = -0.59

Factor a perfect square on the left side:
(z + -0.1)(z + -0.1) = -0.59

Can't calculate square root of the right side.

The solution to this equation could not be determined.