7z-z(4-3z)=35

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Solution for 7z-z(4-3z)=35 equation:


Simplifying
7z + -1z(4 + -3z) = 35
7z + (4 * -1z + -3z * -1z) = 35
7z + (-4z + 3z2) = 35

Combine like terms: 7z + -4z = 3z
3z + 3z2 = 35

Solving
3z + 3z2 = 35

Solving for variable 'z'.

Reorder the terms:
-35 + 3z + 3z2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + 3z + 3z2 = 0

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

Divide each side by '3'.
-11.66666667 + z + z2 = 0

Move the constant term to the right:

Add '11.66666667' to each side of the equation.
-11.66666667 + z + 11.66666667 + z2 = 0 + 11.66666667

Reorder the terms:
-11.66666667 + 11.66666667 + z + z2 = 0 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + z + z2 = 0 + 11.66666667
z + z2 = 0 + 11.66666667

Combine like terms: 0 + 11.66666667 = 11.66666667
z + z2 = 11.66666667

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + z2 = 11.66666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + z2 = 11.66666667 + 0.25

Combine like terms: 11.66666667 + 0.25 = 11.91666667
1.25 + z2 = 11.91666667

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = 11.91666667

Calculate the square root of the right side: 3.45205253

Break this problem into two subproblems by setting 
(z + 0.5) equal to 3.45205253 and -3.45205253.

Subproblem 1

z + 0.5 = 3.45205253 Simplifying z + 0.5 = 3.45205253 Reorder the terms: 0.5 + z = 3.45205253 Solving 0.5 + z = 3.45205253 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = 3.45205253 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = 3.45205253 + -0.5 z = 3.45205253 + -0.5 Combine like terms: 3.45205253 + -0.5 = 2.95205253 z = 2.95205253 Simplifying z = 2.95205253

Subproblem 2

z + 0.5 = -3.45205253 Simplifying z + 0.5 = -3.45205253 Reorder the terms: 0.5 + z = -3.45205253 Solving 0.5 + z = -3.45205253 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = -3.45205253 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = -3.45205253 + -0.5 z = -3.45205253 + -0.5 Combine like terms: -3.45205253 + -0.5 = -3.95205253 z = -3.95205253 Simplifying z = -3.95205253

Solution

The solution to the problem is based on the solutions from the subproblems. z = {2.95205253, -3.95205253}

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