42(x+1)+42x=13x(x+1)

Solution for 42(x+1)+42x=13x(x+1) equation:

Simplifying
42(x + 1) + 42x = 13x(x + 1)

Reorder the terms:
42(1 + x) + 42x = 13x(x + 1)
(1 * 42 + x * 42) + 42x = 13x(x + 1)
(42 + 42x) + 42x = 13x(x + 1)

Combine like terms: 42x + 42x = 84x
42 + 84x = 13x(x + 1)

Reorder the terms:
42 + 84x = 13x(1 + x)
42 + 84x = (1 * 13x + x * 13x)
42 + 84x = (13x + 13x2)

Solving
42 + 84x = 13x + 13x2

Solving for variable 'x'.

Combine like terms: 84x + -13x = 71x
42 + 71x + -13x2 = 13x + 13x2 + -13x + -13x2

Reorder the terms:
42 + 71x + -13x2 = 13x + -13x + 13x2 + -13x2

Combine like terms: 13x + -13x = 0
42 + 71x + -13x2 = 0 + 13x2 + -13x2
42 + 71x + -13x2 = 13x2 + -13x2

Combine like terms: 13x2 + -13x2 = 0
42 + 71x + -13x2 = 0

Factor a trinomial.
(6 + -1x)(7 + 13x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(7 + 13x)' equal to zero and attempt to solve:

Simplifying
7 + 13x = 0

Solving
7 + 13x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 13x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 13x = 0 + -7
13x = 0 + -7

Combine like terms: 0 + -7 = -7
13x = -7

Divide each side by '13'.
x = -0.5384615385

Simplifying
x = -0.5384615385
Solution
x = {6, -0.5384615385}