(x+3)(7x-1)=x+3

Solution for (x+3)(7x-1)=x+3 equation:

Simplifying
(x + 3)(7x + -1) = x + 3

Reorder the terms:
(3 + x)(7x + -1) = x + 3

Reorder the terms:
(3 + x)(-1 + 7x) = x + 3

Multiply (3 + x) * (-1 + 7x)
(3(-1 + 7x) + x(-1 + 7x)) = x + 3
((-1 * 3 + 7x * 3) + x(-1 + 7x)) = x + 3
((-3 + 21x) + x(-1 + 7x)) = x + 3
(-3 + 21x + (-1 * x + 7x * x)) = x + 3
(-3 + 21x + (-1x + 7x2)) = x + 3

Combine like terms: 21x + -1x = 20x
(-3 + 20x + 7x2) = x + 3

Reorder the terms:
-3 + 20x + 7x2 = 3 + x

Solving
-3 + 20x + 7x2 = 3 + x

Solving for variable 'x'.

Reorder the terms:
-3 + -3 + 20x + -1x + 7x2 = 3 + x + -3 + -1x

Combine like terms: -3 + -3 = -6
-6 + 20x + -1x + 7x2 = 3 + x + -3 + -1x

Combine like terms: 20x + -1x = 19x
-6 + 19x + 7x2 = 3 + x + -3 + -1x

Reorder the terms:
-6 + 19x + 7x2 = 3 + -3 + x + -1x

Combine like terms: 3 + -3 = 0
-6 + 19x + 7x2 = 0 + x + -1x
-6 + 19x + 7x2 = x + -1x

Combine like terms: x + -1x = 0
-6 + 19x + 7x2 = 0

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

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 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 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 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
Solution
x = {-3, 0.2857142857}