4n^2+3n-6=7

Simple and best practice solution for 4n^2+3n-6=7 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 4n^2+3n-6=7 equation:


Simplifying
4n2 + 3n + -6 = 7

Reorder the terms:
-6 + 3n + 4n2 = 7

Solving
-6 + 3n + 4n2 = 7

Solving for variable 'n'.

Reorder the terms:
-6 + -7 + 3n + 4n2 = 7 + -7

Combine like terms: -6 + -7 = -13
-13 + 3n + 4n2 = 7 + -7

Combine like terms: 7 + -7 = 0
-13 + 3n + 4n2 = 0

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

Divide each side by '4'.
-3.25 + 0.75n + n2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + 0.75n + 3.25 + n2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + 0.75n + n2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + 0.75n + n2 = 0 + 3.25
0.75n + n2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
0.75n + n2 = 3.25

The n term is 0.75n.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75n + 0.140625 + n2 = 3.25 + 0.140625

Reorder the terms:
0.140625 + 0.75n + n2 = 3.25 + 0.140625

Combine like terms: 3.25 + 0.140625 = 3.390625
0.140625 + 0.75n + n2 = 3.390625

Factor a perfect square on the left side:
(n + 0.375)(n + 0.375) = 3.390625

Calculate the square root of the right side: 1.841364983

Break this problem into two subproblems by setting 
(n + 0.375) equal to 1.841364983 and -1.841364983.

Subproblem 1

n + 0.375 = 1.841364983 Simplifying n + 0.375 = 1.841364983 Reorder the terms: 0.375 + n = 1.841364983 Solving 0.375 + n = 1.841364983 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + n = 1.841364983 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + n = 1.841364983 + -0.375 n = 1.841364983 + -0.375 Combine like terms: 1.841364983 + -0.375 = 1.466364983 n = 1.466364983 Simplifying n = 1.466364983

Subproblem 2

n + 0.375 = -1.841364983 Simplifying n + 0.375 = -1.841364983 Reorder the terms: 0.375 + n = -1.841364983 Solving 0.375 + n = -1.841364983 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + n = -1.841364983 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + n = -1.841364983 + -0.375 n = -1.841364983 + -0.375 Combine like terms: -1.841364983 + -0.375 = -2.216364983 n = -2.216364983 Simplifying n = -2.216364983

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.466364983, -2.216364983}

See similar equations:

| -6.2(3p+6)-2.1(2p-4)= | | 5m=10m+45 | | 9x-2=90 | | (-13)(-4)= | | 5tanx=3tanx+2 | | 7x-4=f(x) | | 13n=9 | | 6m-2=5m | | (8)(n)(3)=64 | | -5-(3-5p)= | | 6p+3r+4p-3r+6= | | 3n+n-9=27 | | -5(4y-6)+2(3y+6)= | | 18=-2+6-m | | -4y^2+9y=-6 | | 6n+4n+2=62 | | ((5)/(3t-1))2 | | 69=3 | | 5/3t-12 | | 3x-5+80+x+9=180 | | 4x-2(x-2)=-8+5x-3 | | Y=-0.8x+12x+25.8 | | 2n-n+8=18 | | 5(x+10)=950 | | y=0.5x^2-8x+1 | | x+35=3c+5 | | (24-2x-x^2)^(1/3) | | 22(12+5)=-5 | | 1/3n=18 | | 8n+2n-15=25 | | 3m+16=6m+4 | | .5y-.66=.66y+.5 |

Equations solver categories