4x(x+1)-3=13

Simple and best practice solution for 4x(x+1)-3=13 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 4x(x+1)-3=13 equation: 


Simplifying
4x(x + 1) + -3 = 13

Reorder the terms:
4x(1 + x) + -3 = 13
(1 * 4x + x * 4x) + -3 = 13
(4x + 4x2) + -3 = 13

Reorder the terms:
-3 + 4x + 4x2 = 13

Solving
-3 + 4x + 4x2 = 13

Solving for variable 'x'.

Reorder the terms:
-3 + -13 + 4x + 4x2 = 13 + -13

Combine like terms: -3 + -13 = -16
-16 + 4x + 4x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-16 + 4x + 4x2 = 0

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

Ignore the factor 4.

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

Simplifying
-4 + x + x2 = 0

Solving
-4 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x + x2 = 0 + 4
x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
x + x2 = 4

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 4 + 0.25

Reorder the terms:
0.25 + x + x2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + x + x2 = 4.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
x + 0.5 = 2.061552813

Simplifying
x + 0.5 = 2.061552813

Reorder the terms:
0.5 + x = 2.061552813

Solving
0.5 + x = 2.061552813

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.061552813 + -0.5
x = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
x = 1.561552813

Simplifying
x = 1.561552813


Subproblem 2
x + 0.5 = -2.061552813

Simplifying
x + 0.5 = -2.061552813

Reorder the terms:
0.5 + x = -2.061552813

Solving
0.5 + x = -2.061552813

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.061552813 + -0.5
x = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
x = -2.561552813

Simplifying
x = -2.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.561552813, -2.561552813}
Solution
x = {1.561552813, -2.561552813}

See similar equations:

| -6=2(a-5) | | +7=42 | | 15-17x+4x^2=0 | | 55+5x=180 | | -4(2x-3)=-4x-16 | | n-26=-40 | | 7x+6-2(5+3x/2)=5x-11 | | -1/5(6x-7/10)=47/50 | | 2x-7=3+4 | | 8n(-2n-3)=12 | | 3x+14=7(x+2)-4x | | 4(x+3)=12(x+1) | | 4p-21=58 | | 3/x+5=-2/x-2 | | -7(2-4x)=7(7x+1) | | -6/5+(-1/5)= | | (4+2/6) | | 1/3(7y+5)=3y-5 | | 1/3(2/5-2/7) | | 10(-41/2)+3=6(-41/2)-15 | | 2/3y-6=13 | | 3/4-1-3z=1/4 | | -1/9c=-8 | | 3d^2+22=52 | | 4x(13)= | | 6(17q+3)= | | (7x^2+1)/(7x) | | (3x+5)+(10x-7)=180 | | 4z-7=3+10 | | 2x^2+12=-11x | | 15(p+1+4q)= | | 10-3y=31 |

Equations solver categories