7x(x+3)=14x+42

Solution for 7x(x+3)=14x+42 equation:

Simplifying
7x(x + 3) = 14x + 42

Reorder the terms:
7x(3 + x) = 14x + 42
(3 * 7x + x * 7x) = 14x + 42
(21x + 7x2) = 14x + 42

Reorder the terms:
21x + 7x2 = 42 + 14x

Solving
21x + 7x2 = 42 + 14x

Solving for variable 'x'.

Reorder the terms:
-42 + 21x + -14x + 7x2 = 42 + 14x + -42 + -14x

Combine like terms: 21x + -14x = 7x
-42 + 7x + 7x2 = 42 + 14x + -42 + -14x

Reorder the terms:
-42 + 7x + 7x2 = 42 + -42 + 14x + -14x

Combine like terms: 42 + -42 = 0
-42 + 7x + 7x2 = 0 + 14x + -14x
-42 + 7x + 7x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-42 + 7x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + x + x2) = 0

Factor a trinomial.
7((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 7.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}