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

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

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

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

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

Reorder the terms for easier multiplication:
5 * 3(-1 + 3z)(2 + z) = 4(2 + 1)

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

Multiply (-1 + 3z) * (2 + z)
15(-1(2 + z) + 3z * (2 + z)) = 4(2 + 1)
15((2 * -1 + z * -1) + 3z * (2 + z)) = 4(2 + 1)
15((-2 + -1z) + 3z * (2 + z)) = 4(2 + 1)
15(-2 + -1z + (2 * 3z + z * 3z)) = 4(2 + 1)
15(-2 + -1z + (6z + 3z2)) = 4(2 + 1)

Combine like terms: -1z + 6z = 5z
15(-2 + 5z + 3z2) = 4(2 + 1)
(-2 * 15 + 5z * 15 + 3z2 * 15) = 4(2 + 1)
(-30 + 75z + 45z2) = 4(2 + 1)

Combine like terms: 2 + 1 = 3
-30 + 75z + 45z2 = 4(3)

Multiply 4 * 3
-30 + 75z + 45z2 = 12

Solving
-30 + 75z + 45z2 = 12

Solving for variable 'z'.

Reorder the terms:
-30 + -12 + 75z + 45z2 = 12 + -12

Combine like terms: -30 + -12 = -42
-42 + 75z + 45z2 = 12 + -12

Combine like terms: 12 + -12 = 0
-42 + 75z + 45z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 25z + 15z2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-14 + 25z + 15z2)' equal to zero and attempt to solve:

Simplifying
-14 + 25z + 15z2 = 0

Solving
-14 + 25z + 15z2 = 0

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

Divide each side by '15'.
-0.9333333333 + 1.666666667z + z2 = 0

Move the constant term to the right:

Add '0.9333333333' to each side of the equation.
-0.9333333333 + 1.666666667z + 0.9333333333 + z2 = 0 + 0.9333333333

Reorder the terms:
-0.9333333333 + 0.9333333333 + 1.666666667z + z2 = 0 + 0.9333333333

Combine like terms: -0.9333333333 + 0.9333333333 = 0.0000000000
0.0000000000 + 1.666666667z + z2 = 0 + 0.9333333333
1.666666667z + z2 = 0 + 0.9333333333

Combine like terms: 0 + 0.9333333333 = 0.9333333333
1.666666667z + z2 = 0.9333333333

The z term is 1.666666667z.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667z + 0.6944444447 + z2 = 0.9333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667z + z2 = 0.9333333333 + 0.6944444447

Combine like terms: 0.9333333333 + 0.6944444447 = 1.627777778
0.6944444447 + 1.666666667z + z2 = 1.627777778

Factor a perfect square on the left side:
(z + 0.8333333335)(z + 0.8333333335) = 1.627777778

Calculate the square root of the right side: 1.275843947

Break this problem into two subproblems by setting 
(z + 0.8333333335) equal to 1.275843947 and -1.275843947.

Subproblem 1
z + 0.8333333335 = 1.275843947

Simplifying
z + 0.8333333335 = 1.275843947

Reorder the terms:
0.8333333335 + z = 1.275843947

Solving
0.8333333335 + z = 1.275843947

Solving for variable 'z'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + z = 1.275843947 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + z = 1.275843947 + -0.8333333335
z = 1.275843947 + -0.8333333335

Combine like terms: 1.275843947 + -0.8333333335 = 0.4425106135
z = 0.4425106135

Simplifying
z = 0.4425106135

Subproblem 2
z + 0.8333333335 = -1.275843947

Simplifying
z + 0.8333333335 = -1.275843947

Reorder the terms:
0.8333333335 + z = -1.275843947

Solving
0.8333333335 + z = -1.275843947

Solving for variable 'z'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + z = -1.275843947 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + z = -1.275843947 + -0.8333333335
z = -1.275843947 + -0.8333333335

Combine like terms: -1.275843947 + -0.8333333335 = -2.1091772805
z = -2.1091772805

Simplifying
z = -2.1091772805

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.4425106135, -2.1091772805}
Solution
z = {0.4425106135, -2.1091772805}