2(6z-3)(5+4z)=(12z-5)(2z+1)

Solution for 2(6z-3)(5+4z)=(12z-5)(2z+1) equation:

Simplifying
2(6z + -3)(5 + 4z) = (12z + -5)(2z + 1)

Reorder the terms:
2(-3 + 6z)(5 + 4z) = (12z + -5)(2z + 1)

Multiply (-3 + 6z) * (5 + 4z)
2(-3(5 + 4z) + 6z * (5 + 4z)) = (12z + -5)(2z + 1)
2((5 * -3 + 4z * -3) + 6z * (5 + 4z)) = (12z + -5)(2z + 1)
2((-15 + -12z) + 6z * (5 + 4z)) = (12z + -5)(2z + 1)
2(-15 + -12z + (5 * 6z + 4z * 6z)) = (12z + -5)(2z + 1)
2(-15 + -12z + (30z + 24z2)) = (12z + -5)(2z + 1)

Combine like terms: -12z + 30z = 18z
2(-15 + 18z + 24z2) = (12z + -5)(2z + 1)
(-15 * 2 + 18z * 2 + 24z2 * 2) = (12z + -5)(2z + 1)
(-30 + 36z + 48z2) = (12z + -5)(2z + 1)

Reorder the terms:
-30 + 36z + 48z2 = (-5 + 12z)(2z + 1)

Reorder the terms:
-30 + 36z + 48z2 = (-5 + 12z)(1 + 2z)

Multiply (-5 + 12z) * (1 + 2z)
-30 + 36z + 48z2 = (-5(1 + 2z) + 12z * (1 + 2z))
-30 + 36z + 48z2 = ((1 * -5 + 2z * -5) + 12z * (1 + 2z))
-30 + 36z + 48z2 = ((-5 + -10z) + 12z * (1 + 2z))
-30 + 36z + 48z2 = (-5 + -10z + (1 * 12z + 2z * 12z))
-30 + 36z + 48z2 = (-5 + -10z + (12z + 24z2))

Combine like terms: -10z + 12z = 2z
-30 + 36z + 48z2 = (-5 + 2z + 24z2)

Solving
-30 + 36z + 48z2 = -5 + 2z + 24z2

Solving for variable 'z'.

Reorder the terms:
-30 + 5 + 36z + -2z + 48z2 + -24z2 = -5 + 2z + 24z2 + 5 + -2z + -24z2

Combine like terms: -30 + 5 = -25
-25 + 36z + -2z + 48z2 + -24z2 = -5 + 2z + 24z2 + 5 + -2z + -24z2

Combine like terms: 36z + -2z = 34z
-25 + 34z + 48z2 + -24z2 = -5 + 2z + 24z2 + 5 + -2z + -24z2

Combine like terms: 48z2 + -24z2 = 24z2
-25 + 34z + 24z2 = -5 + 2z + 24z2 + 5 + -2z + -24z2

Reorder the terms:
-25 + 34z + 24z2 = -5 + 5 + 2z + -2z + 24z2 + -24z2

Combine like terms: -5 + 5 = 0
-25 + 34z + 24z2 = 0 + 2z + -2z + 24z2 + -24z2
-25 + 34z + 24z2 = 2z + -2z + 24z2 + -24z2

Combine like terms: 2z + -2z = 0
-25 + 34z + 24z2 = 0 + 24z2 + -24z2
-25 + 34z + 24z2 = 24z2 + -24z2

Combine like terms: 24z2 + -24z2 = 0
-25 + 34z + 24z2 = 0

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

Divide each side by '24'.
-1.041666667 + 1.416666667z + z2 = 0

Move the constant term to the right:

Add '1.041666667' to each side of the equation.
-1.041666667 + 1.416666667z + 1.041666667 + z2 = 0 + 1.041666667

Reorder the terms:
-1.041666667 + 1.041666667 + 1.416666667z + z2 = 0 + 1.041666667

Combine like terms: -1.041666667 + 1.041666667 = 0.000000000
0.000000000 + 1.416666667z + z2 = 0 + 1.041666667
1.416666667z + z2 = 0 + 1.041666667

Combine like terms: 0 + 1.041666667 = 1.041666667
1.416666667z + z2 = 1.041666667

The z term is 1.416666667z.  Take half its coefficient (0.7083333335).
Square it (0.5017361113) and add it to both sides.

Add '0.5017361113' to each side of the equation.
1.416666667z + 0.5017361113 + z2 = 1.041666667 + 0.5017361113

Reorder the terms:
0.5017361113 + 1.416666667z + z2 = 1.041666667 + 0.5017361113

Combine like terms: 1.041666667 + 0.5017361113 = 1.5434027783
0.5017361113 + 1.416666667z + z2 = 1.5434027783

Factor a perfect square on the left side:
(z + 0.7083333335)(z + 0.7083333335) = 1.5434027783

Calculate the square root of the right side: 1.242337627

Break this problem into two subproblems by setting 
(z + 0.7083333335) equal to 1.242337627 and -1.242337627.

Subproblem 1
z + 0.7083333335 = 1.242337627

Simplifying
z + 0.7083333335 = 1.242337627

Reorder the terms:
0.7083333335 + z = 1.242337627

Solving
0.7083333335 + z = 1.242337627

Solving for variable 'z'.

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

Add '-0.7083333335' to each side of the equation.
0.7083333335 + -0.7083333335 + z = 1.242337627 + -0.7083333335

Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000
0.0000000000 + z = 1.242337627 + -0.7083333335
z = 1.242337627 + -0.7083333335

Combine like terms: 1.242337627 + -0.7083333335 = 0.5340042935
z = 0.5340042935

Simplifying
z = 0.5340042935

Subproblem 2
z + 0.7083333335 = -1.242337627

Simplifying
z + 0.7083333335 = -1.242337627

Reorder the terms:
0.7083333335 + z = -1.242337627

Solving
0.7083333335 + z = -1.242337627

Solving for variable 'z'.

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

Add '-0.7083333335' to each side of the equation.
0.7083333335 + -0.7083333335 + z = -1.242337627 + -0.7083333335

Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000
0.0000000000 + z = -1.242337627 + -0.7083333335
z = -1.242337627 + -0.7083333335

Combine like terms: -1.242337627 + -0.7083333335 = -1.9506709605
z = -1.9506709605

Simplifying
z = -1.9506709605

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.5340042935, -1.9506709605}