(2x-1)(x+4)=x

Simple and best practice solution for (2x-1)(x+4)=x 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 (2x-1)(x+4)=x equation: 


Simplifying
(2x + -1)(x + 4) = x

Reorder the terms:
(-1 + 2x)(x + 4) = x

Reorder the terms:
(-1 + 2x)(4 + x) = x

Multiply (-1 + 2x) * (4 + x)
(-1(4 + x) + 2x * (4 + x)) = x
((4 * -1 + x * -1) + 2x * (4 + x)) = x
((-4 + -1x) + 2x * (4 + x)) = x
(-4 + -1x + (4 * 2x + x * 2x)) = x
(-4 + -1x + (8x + 2x2)) = x

Combine like terms: -1x + 8x = 7x
(-4 + 7x + 2x2) = x

Solving
-4 + 7x + 2x2 = x

Solving for variable 'x'.

Reorder the terms:
-4 + 7x + -1x + 2x2 = x + -1x

Combine like terms: 7x + -1x = 6x
-4 + 6x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-4 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + 3x + x2 = 0

Solving
-2 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 3x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 3x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3x + x2 = 0 + 2
3x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
3x + x2 = 2

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 2 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + 3x + x2 = 4.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
x + 1.5 = 2.061552813

Simplifying
x + 1.5 = 2.061552813

Reorder the terms:
1.5 + x = 2.061552813

Solving
1.5 + x = 2.061552813

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.061552813 + -1.5
x = 2.061552813 + -1.5

Combine like terms: 2.061552813 + -1.5 = 0.561552813
x = 0.561552813

Simplifying
x = 0.561552813


Subproblem 2
x + 1.5 = -2.061552813

Simplifying
x + 1.5 = -2.061552813

Reorder the terms:
1.5 + x = -2.061552813

Solving
1.5 + x = -2.061552813

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.061552813 + -1.5
x = -2.061552813 + -1.5

Combine like terms: -2.061552813 + -1.5 = -3.561552813
x = -3.561552813

Simplifying
x = -3.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.561552813, -3.561552813}
Solution
x = {0.561552813, -3.561552813}

See similar equations:

| 9x+2x-6x-5=5 | | n^2+22n+105=0 | | 32+6x+7x=-15+28 | | -6+11=-5 | | 8+8f-9-9f= | | 6t-2t+-4=3t+3 | | 5(2-8x)+4=-306 | | -18+11=-5 | | 3t-6pt+1t+1t-5pt= | | 9z=12-48 | | -14n+1=rat-4n | | 3x+4*x=4 | | -17c+29=-379 | | y=x^4-5x^2-36 | | 25n+110=12(n+4) | | 6b=16 | | 4x/5=28 | | -20(v+47)=-820 | | -5r+8r= | | 25n+110=12n | | 6(2x+5)=2(4x+15) | | -6(1+2x)=-27 | | 40+15+.25x=45+45+.35 | | 6t-2t+4=3t+2 | | .33(6z-12)=4(.5x+1)-2 | | 7y-1=4y+27 | | 3x+5(x+2)=34 | | 7*(13-6)=49 | | 5(6+m)=-3m+4(2M-5) | | -2(5s-6)-12=-3(6s+4)-5 | | 3x-1=(4) | | 29(c+27)=899 |

Equations solver categories