4x(x+7)=2x+46

Solution for 4x(x+7)=2x+46 equation:

Simplifying
4x(x + 7) = 2x + 46

Reorder the terms:
4x(7 + x) = 2x + 46
(7 * 4x + x * 4x) = 2x + 46
(28x + 4x2) = 2x + 46

Reorder the terms:
28x + 4x2 = 46 + 2x

Solving
28x + 4x2 = 46 + 2x

Solving for variable 'x'.

Reorder the terms:
-46 + 28x + -2x + 4x2 = 46 + 2x + -46 + -2x

Combine like terms: 28x + -2x = 26x
-46 + 26x + 4x2 = 46 + 2x + -46 + -2x

Reorder the terms:
-46 + 26x + 4x2 = 46 + -46 + 2x + -2x

Combine like terms: 46 + -46 = 0
-46 + 26x + 4x2 = 0 + 2x + -2x
-46 + 26x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-46 + 26x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-23 + 13x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-23 + 13x + 2x2)' equal to zero and attempt to solve:

Simplifying
-23 + 13x + 2x2 = 0

Solving
-23 + 13x + 2x2 = 0

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

Divide each side by '2'.
-11.5 + 6.5x + x2 = 0

Move the constant term to the right:

Add '11.5' to each side of the equation.
-11.5 + 6.5x + 11.5 + x2 = 0 + 11.5

Reorder the terms:
-11.5 + 11.5 + 6.5x + x2 = 0 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + 6.5x + x2 = 0 + 11.5
6.5x + x2 = 0 + 11.5

Combine like terms: 0 + 11.5 = 11.5
6.5x + x2 = 11.5

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = 11.5 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 11.5 + 10.5625

Combine like terms: 11.5 + 10.5625 = 22.0625
10.5625 + 6.5x + x2 = 22.0625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 22.0625

Calculate the square root of the right side: 4.697073557

Break this problem into two subproblems by setting 
(x + 3.25) equal to 4.697073557 and -4.697073557.

Subproblem 1
x + 3.25 = 4.697073557

Simplifying
x + 3.25 = 4.697073557

Reorder the terms:
3.25 + x = 4.697073557

Solving
3.25 + x = 4.697073557

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = 4.697073557 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 4.697073557 + -3.25
x = 4.697073557 + -3.25

Combine like terms: 4.697073557 + -3.25 = 1.447073557
x = 1.447073557

Simplifying
x = 1.447073557

Subproblem 2
x + 3.25 = -4.697073557

Simplifying
x + 3.25 = -4.697073557

Reorder the terms:
3.25 + x = -4.697073557

Solving
3.25 + x = -4.697073557

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = -4.697073557 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -4.697073557 + -3.25
x = -4.697073557 + -3.25

Combine like terms: -4.697073557 + -3.25 = -7.947073557
x = -7.947073557

Simplifying
x = -7.947073557

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.447073557, -7.947073557}
Solution
x = {1.447073557, -7.947073557}