7x(4x+6)=21

Simple and best practice solution for 7x(4x+6)=21 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 7x(4x+6)=21 equation: 


Simplifying
7x(4x + 6) = 21

Reorder the terms:
7x(6 + 4x) = 21
(6 * 7x + 4x * 7x) = 21
(42x + 28x2) = 21

Solving
42x + 28x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + 42x + 28x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 42x + 28x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + 6x + 4x2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-3 + 6x + 4x2)' equal to zero and attempt to solve:

Simplifying
-3 + 6x + 4x2 = 0

Solving
-3 + 6x + 4x2 = 0

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

Divide each side by '4'.
-0.75 + 1.5x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 1.5x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 1.5x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 1.5x + x2 = 0 + 0.75
1.5x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
1.5x + x2 = 0.75

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 0.75 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 0.75 + 0.5625

Combine like terms: 0.75 + 0.5625 = 1.3125
0.5625 + 1.5x + x2 = 1.3125

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 1.3125

Calculate the square root of the right side: 1.145643924

Break this problem into two subproblems by setting 
(x + 0.75) equal to 1.145643924 and -1.145643924.


Subproblem 1
x + 0.75 = 1.145643924

Simplifying
x + 0.75 = 1.145643924

Reorder the terms:
0.75 + x = 1.145643924

Solving
0.75 + x = 1.145643924

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 1.145643924 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 1.145643924 + -0.75
x = 1.145643924 + -0.75

Combine like terms: 1.145643924 + -0.75 = 0.395643924
x = 0.395643924

Simplifying
x = 0.395643924


Subproblem 2
x + 0.75 = -1.145643924

Simplifying
x + 0.75 = -1.145643924

Reorder the terms:
0.75 + x = -1.145643924

Solving
0.75 + x = -1.145643924

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -1.145643924 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -1.145643924 + -0.75
x = -1.145643924 + -0.75

Combine like terms: -1.145643924 + -0.75 = -1.895643924
x = -1.895643924

Simplifying
x = -1.895643924


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.395643924, -1.895643924}
Solution
x = {0.395643924, -1.895643924}

See similar equations:

| 21/w=-7 | | 145=x+2+21 | | 9x(5x+5)=27 | | 145=(x+2)+21 | | 1=-(1+10y)-8y | | -x^2+x=-2 | | 180-x=3.5(x) | | 2a^2-10=-23 | | -(-10n+1)=-5(1-6n)+7 | | -x^2+6=-2 | | 2x^2-10x-10.5=0 | | (1/5)(1/5)(1/5)(1/5)(1/5)(1/5) | | 3(x-2)+5(2x+3)=35 | | 6x+11-9x=16-18x+15-5 | | 3y-4=4y-11 | | -2-7q=-(2q-4) | | 4x-12-7x-42=-1 | | (6x^2y-3xy+5xy^2)-(3x^2y+5xy+4xy^2)= | | 4-7n=4(3n-5) | | 8(4y-5)-7a=20y-10 | | x^2-11=14 | | n=f+h+x/6 | | -1=z+3 | | -6x-36+4=-64 | | (2x+7)(2x^2-7x+5)=0 | | (2xy)(36x)= | | (x+2)=x-18 | | -7/x-3 | | 5-x=0.5x+4 | | 6.5/1=x/365 | | -29+x=x+24 | | x-13=1988 |

Equations solver categories