4x(x+2)=10x+24

Solution for 4x(x+2)=10x+24 equation:

Simplifying
4x(x + 2) = 10x + 24

Reorder the terms:
4x(2 + x) = 10x + 24
(2 * 4x + x * 4x) = 10x + 24
(8x + 4x2) = 10x + 24

Reorder the terms:
8x + 4x2 = 24 + 10x

Solving
8x + 4x2 = 24 + 10x

Solving for variable 'x'.

Reorder the terms:
-24 + 8x + -10x + 4x2 = 24 + 10x + -24 + -10x

Combine like terms: 8x + -10x = -2x
-24 + -2x + 4x2 = 24 + 10x + -24 + -10x

Reorder the terms:
-24 + -2x + 4x2 = 24 + -24 + 10x + -10x

Combine like terms: 24 + -24 = 0
-24 + -2x + 4x2 = 0 + 10x + -10x
-24 + -2x + 4x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-24 + -2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -1x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + -1x + 2x2)' equal to zero and attempt to solve:

Simplifying
-12 + -1x + 2x2 = 0

Solving
-12 + -1x + 2x2 = 0

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

Divide each side by '2'.
-6 + -0.5x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -0.5x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -0.5x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -0.5x + x2 = 0 + 6
-0.5x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-0.5x + x2 = 6

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 6 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 6 + 0.0625

Combine like terms: 6 + 0.0625 = 6.0625
0.0625 + -0.5x + x2 = 6.0625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(x + -0.25) equal to 2.46221445 and -2.46221445.

Subproblem 1
x + -0.25 = 2.46221445

Simplifying
x + -0.25 = 2.46221445

Reorder the terms:
-0.25 + x = 2.46221445

Solving
-0.25 + x = 2.46221445

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 2.46221445 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 2.46221445 + 0.25
x = 2.46221445 + 0.25

Combine like terms: 2.46221445 + 0.25 = 2.71221445
x = 2.71221445

Simplifying
x = 2.71221445

Subproblem 2
x + -0.25 = -2.46221445

Simplifying
x + -0.25 = -2.46221445

Reorder the terms:
-0.25 + x = -2.46221445

Solving
-0.25 + x = -2.46221445

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -2.46221445 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -2.46221445 + 0.25
x = -2.46221445 + 0.25

Combine like terms: -2.46221445 + 0.25 = -2.21221445
x = -2.21221445

Simplifying
x = -2.21221445

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.71221445, -2.21221445}
Solution
x = {2.71221445, -2.21221445}