2x(x+7)=6x+18

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Solution for 2x(x+7)=6x+18 equation: 


Simplifying
2x(x + 7) = 6x + 18

Reorder the terms:
2x(7 + x) = 6x + 18
(7 * 2x + x * 2x) = 6x + 18
(14x + 2x2) = 6x + 18

Reorder the terms:
14x + 2x2 = 18 + 6x

Solving
14x + 2x2 = 18 + 6x

Solving for variable 'x'.

Reorder the terms:
-18 + 14x + -6x + 2x2 = 18 + 6x + -18 + -6x

Combine like terms: 14x + -6x = 8x
-18 + 8x + 2x2 = 18 + 6x + -18 + -6x

Reorder the terms:
-18 + 8x + 2x2 = 18 + -18 + 6x + -6x

Combine like terms: 18 + -18 = 0
-18 + 8x + 2x2 = 0 + 6x + -6x
-18 + 8x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-18 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + 4x + x2 = 0

Solving
-9 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 4x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 4x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 4x + x2 = 0 + 9
4x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
4x + x2 = 9

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 9 + 4

Reorder the terms:
4 + 4x + x2 = 9 + 4

Combine like terms: 9 + 4 = 13
4 + 4x + x2 = 13

Factor a perfect square on the left side:
(x + 2)(x + 2) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 2) equal to 3.605551275 and -3.605551275.


Subproblem 1
x + 2 = 3.605551275

Simplifying
x + 2 = 3.605551275

Reorder the terms:
2 + x = 3.605551275

Solving
2 + x = 3.605551275

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 3.605551275 + -2

Combine like terms: 2 + -2 = 0
0 + x = 3.605551275 + -2
x = 3.605551275 + -2

Combine like terms: 3.605551275 + -2 = 1.605551275
x = 1.605551275

Simplifying
x = 1.605551275


Subproblem 2
x + 2 = -3.605551275

Simplifying
x + 2 = -3.605551275

Reorder the terms:
2 + x = -3.605551275

Solving
2 + x = -3.605551275

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -3.605551275 + -2

Combine like terms: 2 + -2 = 0
0 + x = -3.605551275 + -2
x = -3.605551275 + -2

Combine like terms: -3.605551275 + -2 = -5.605551275
x = -5.605551275

Simplifying
x = -5.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.605551275, -5.605551275}
Solution
x = {1.605551275, -5.605551275}

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