(2x)(x+9)=x(x+7)+42

Solution for (2x)(x+9)=x(x+7)+42 equation:

Simplifying
(2x)(x + 9) = x(x + 7) + 42

Remove parenthesis around (2x)
2x(x + 9) = x(x + 7) + 42

Reorder the terms:
2x(9 + x) = x(x + 7) + 42
(9 * 2x + x * 2x) = x(x + 7) + 42
(18x + 2x2) = x(x + 7) + 42

Reorder the terms:
18x + 2x2 = x(7 + x) + 42
18x + 2x2 = (7 * x + x * x) + 42
18x + 2x2 = (7x + x2) + 42

Reorder the terms:
18x + 2x2 = 42 + 7x + x2

Solving
18x + 2x2 = 42 + 7x + x2

Solving for variable 'x'.

Reorder the terms:
-42 + 18x + -7x + 2x2 + -1x2 = 42 + 7x + x2 + -42 + -7x + -1x2

Combine like terms: 18x + -7x = 11x
-42 + 11x + 2x2 + -1x2 = 42 + 7x + x2 + -42 + -7x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-42 + 11x + 1x2 = 42 + 7x + x2 + -42 + -7x + -1x2

Reorder the terms:
-42 + 11x + 1x2 = 42 + -42 + 7x + -7x + x2 + -1x2

Combine like terms: 42 + -42 = 0
-42 + 11x + 1x2 = 0 + 7x + -7x + x2 + -1x2
-42 + 11x + 1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
-42 + 11x + 1x2 = 0 + x2 + -1x2
-42 + 11x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-42 + 11x + 1x2 = 0

Factor a trinomial.
(-14 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-14, 3}