3z(z+4)=(z^2+9)

Simple and best practice solution for 3z(z+4)=(z^2+9) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

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


Simplifying
3z(z + 4) = (z2 + 9)

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

Reorder the terms:
12z + 3z2 = (9 + z2)

Remove parenthesis around (9 + z2)
12z + 3z2 = 9 + z2

Solving
12z + 3z2 = 9 + z2

Solving for variable 'z'.

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

Combine like terms: 3z2 + -1z2 = 2z2
-9 + 12z + 2z2 = 9 + z2 + -9 + -1z2

Reorder the terms:
-9 + 12z + 2z2 = 9 + -9 + z2 + -1z2

Combine like terms: 9 + -9 = 0
-9 + 12z + 2z2 = 0 + z2 + -1z2
-9 + 12z + 2z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-9 + 12z + 2z2 = 0

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

Divide each side by '2'.
-4.5 + 6z + z2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 6z + 4.5 + z2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 6z + z2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 6z + z2 = 0 + 4.5
6z + z2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
6z + z2 = 4.5

The z term is 6z.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6z + 9 + z2 = 4.5 + 9

Reorder the terms:
9 + 6z + z2 = 4.5 + 9

Combine like terms: 4.5 + 9 = 13.5
9 + 6z + z2 = 13.5

Factor a perfect square on the left side:
(z + 3)(z + 3) = 13.5

Calculate the square root of the right side: 3.674234614

Break this problem into two subproblems by setting 
(z + 3) equal to 3.674234614 and -3.674234614.

Subproblem 1

z + 3 = 3.674234614 Simplifying z + 3 = 3.674234614 Reorder the terms: 3 + z = 3.674234614 Solving 3 + z = 3.674234614 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = 3.674234614 + -3 Combine like terms: 3 + -3 = 0 0 + z = 3.674234614 + -3 z = 3.674234614 + -3 Combine like terms: 3.674234614 + -3 = 0.674234614 z = 0.674234614 Simplifying z = 0.674234614

Subproblem 2

z + 3 = -3.674234614 Simplifying z + 3 = -3.674234614 Reorder the terms: 3 + z = -3.674234614 Solving 3 + z = -3.674234614 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = -3.674234614 + -3 Combine like terms: 3 + -3 = 0 0 + z = -3.674234614 + -3 z = -3.674234614 + -3 Combine like terms: -3.674234614 + -3 = -6.674234614 z = -6.674234614 Simplifying z = -6.674234614

Solution

The solution to the problem is based on the solutions from the subproblems. z = {0.674234614, -6.674234614}

See similar equations:

| -20x=-20x-3 | | -20x=-20x | | 4x^2-20x+32= | | -8+7b=8b-7 | | 4(3+x)-4=7-2x | | F(3)=-6(3)-3 | | 4-8(9-12)= | | x^3+6x^2-1=0 | | x+24=-17 | | 4(3ab-4)+2(ab+9)= | | X^2+-3=0 | | 23x-32+41=-6 | | v=v+1 | | 2.7p=1.5p+6 | | 6a+2-6+3a-2a+2b= | | 9x-1=4(2x+4)-15 | | 2-4(-2)=-2(3+4(-2)) | | 6h+4h-12-h= | | 3(4+x)=90 | | x+2=3(x-4) | | 0.666666667x-11=4+x | | 80=y^2+8y+16+x^2-8x+16 | | -8+(7+(-12))= | | 4/5*4/5*4/5*4/5*4/5= | | 5x-17=63 | | (8x+5)+(5x-9)=74 | | F(8)=-6(8)-3 | | 4+5h=8+3h | | 10d+10(9)=210 | | 0.9x-2.1=0.6 | | N+5(n-1)=17 | | -4x^2-8+1=0 |

Equations solver categories