5x(3x+14)=4(x+3)

Solution for 5x(3x+14)=4(x+3) equation:

Simplifying
5x(3x + 14) = 4(x + 3)

Reorder the terms:
5x(14 + 3x) = 4(x + 3)
(14 * 5x + 3x * 5x) = 4(x + 3)
(70x + 15x2) = 4(x + 3)

Reorder the terms:
70x + 15x2 = 4(3 + x)
70x + 15x2 = (3 * 4 + x * 4)
70x + 15x2 = (12 + 4x)

Solving
70x + 15x2 = 12 + 4x

Solving for variable 'x'.

Reorder the terms:
-12 + 70x + -4x + 15x2 = 12 + 4x + -12 + -4x

Combine like terms: 70x + -4x = 66x
-12 + 66x + 15x2 = 12 + 4x + -12 + -4x

Reorder the terms:
-12 + 66x + 15x2 = 12 + -12 + 4x + -4x

Combine like terms: 12 + -12 = 0
-12 + 66x + 15x2 = 0 + 4x + -4x
-12 + 66x + 15x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-12 + 66x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 22x + 5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + 22x + 5x2)' equal to zero and attempt to solve:

Simplifying
-4 + 22x + 5x2 = 0

Solving
-4 + 22x + 5x2 = 0

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

Divide each side by '5'.
-0.8 + 4.4x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 4.4x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 4.4x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 4.4x + x2 = 0 + 0.8
4.4x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
4.4x + x2 = 0.8

The x term is 4.4x.  Take half its coefficient (2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
4.4x + 4.84 + x2 = 0.8 + 4.84

Reorder the terms:
4.84 + 4.4x + x2 = 0.8 + 4.84

Combine like terms: 0.8 + 4.84 = 5.64
4.84 + 4.4x + x2 = 5.64

Factor a perfect square on the left side:
(x + 2.2)(x + 2.2) = 5.64

Calculate the square root of the right side: 2.374868417

Break this problem into two subproblems by setting 
(x + 2.2) equal to 2.374868417 and -2.374868417.

Subproblem 1
x + 2.2 = 2.374868417

Simplifying
x + 2.2 = 2.374868417

Reorder the terms:
2.2 + x = 2.374868417

Solving
2.2 + x = 2.374868417

Solving for variable 'x'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + x = 2.374868417 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + x = 2.374868417 + -2.2
x = 2.374868417 + -2.2

Combine like terms: 2.374868417 + -2.2 = 0.174868417
x = 0.174868417

Simplifying
x = 0.174868417

Subproblem 2
x + 2.2 = -2.374868417

Simplifying
x + 2.2 = -2.374868417

Reorder the terms:
2.2 + x = -2.374868417

Solving
2.2 + x = -2.374868417

Solving for variable 'x'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + x = -2.374868417 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + x = -2.374868417 + -2.2
x = -2.374868417 + -2.2

Combine like terms: -2.374868417 + -2.2 = -4.574868417
x = -4.574868417

Simplifying
x = -4.574868417

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.174868417, -4.574868417}
Solution
x = {0.174868417, -4.574868417}