-2z(5z-4)+6z=-4

Simple and best practice solution for -2z(5z-4)+6z=-4 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 -2z(5z-4)+6z=-4 equation: 


Simplifying
-2z(5z + -4) + 6z = -4

Reorder the terms:
-2z(-4 + 5z) + 6z = -4
(-4 * -2z + 5z * -2z) + 6z = -4
(8z + -10z2) + 6z = -4

Reorder the terms:
8z + 6z + -10z2 = -4

Combine like terms: 8z + 6z = 14z
14z + -10z2 = -4

Solving
14z + -10z2 = -4

Solving for variable 'z'.

Reorder the terms:
4 + 14z + -10z2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 14z + -10z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 7z + -5z2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + 7z + -5z2)' equal to zero and attempt to solve:

Simplifying
2 + 7z + -5z2 = 0

Solving
2 + 7z + -5z2 = 0

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

Divide each side by '-5'.
-0.4 + -1.4z + z2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -1.4z + 0.4 + z2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -1.4z + z2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -1.4z + z2 = 0 + 0.4
-1.4z + z2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-1.4z + z2 = 0.4

The z term is -1.4z.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4z + 0.49 + z2 = 0.4 + 0.49

Reorder the terms:
0.49 + -1.4z + z2 = 0.4 + 0.49

Combine like terms: 0.4 + 0.49 = 0.89
0.49 + -1.4z + z2 = 0.89

Factor a perfect square on the left side:
(z + -0.7)(z + -0.7) = 0.89

Calculate the square root of the right side: 0.943398113

Break this problem into two subproblems by setting 
(z + -0.7) equal to 0.943398113 and -0.943398113.


Subproblem 1
z + -0.7 = 0.943398113

Simplifying
z + -0.7 = 0.943398113

Reorder the terms:
-0.7 + z = 0.943398113

Solving
-0.7 + z = 0.943398113

Solving for variable 'z'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + z = 0.943398113 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + z = 0.943398113 + 0.7
z = 0.943398113 + 0.7

Combine like terms: 0.943398113 + 0.7 = 1.643398113
z = 1.643398113

Simplifying
z = 1.643398113


Subproblem 2
z + -0.7 = -0.943398113

Simplifying
z + -0.7 = -0.943398113

Reorder the terms:
-0.7 + z = -0.943398113

Solving
-0.7 + z = -0.943398113

Solving for variable 'z'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + z = -0.943398113 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + z = -0.943398113 + 0.7
z = -0.943398113 + 0.7

Combine like terms: -0.943398113 + 0.7 = -0.243398113
z = -0.243398113

Simplifying
z = -0.243398113


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.643398113, -0.243398113}
Solution
z = {1.643398113, -0.243398113}

See similar equations:

| 2.5r-(2-5r)=2.6+6.1r | | 7x+24=x^2+12 | | 7xy+63x+14y= | | X^2-7=5x | | 5d^2-2d-8=0 | | -2(x-1)+(x-14)=-x-14 | | 12x^2-96x=144 | | 6z+4=9z+9 | | 4.9t+9t+3=0 | | 3z+5=9z+9 | | 3x^2+24x+48=8 | | 100+.30x=80+.80x | | 4p^2=-12p-9 | | 2(3a+4)=6 | | 2a-9=4(3a+1)-6 | | 6x^2+26x=-28 | | 40x^2-88x+48= | | 2(5x-13)-x=3(x-3)+7 | | 2m+6-4m=6 | | 4a-21=7a | | 3(x+1)=4y | | 4x+12=3x-10 | | 2y(x+2x)= | | 8d=-48 | | 3+2x=-41 | | -2(3t-5)+3t=8t-4 | | 8x+5+10x-7=180 | | 6x^2+13x+42.25=28+42.25 | | 5-5-3t= | | 19-n=38 | | 0.54(12)+0.06x=0.18(6+x) | | 5(3x-y)=0 |

Equations solver categories