2x^2+19x+42=x^2+12x+36

Solution for 2x^2+19x+42=x^2+12x+36 equation:

Simplifying
2x2 + 19x + 42 = x2 + 12x + 36

Reorder the terms:
42 + 19x + 2x2 = x2 + 12x + 36

Reorder the terms:
42 + 19x + 2x2 = 36 + 12x + x2

Solving
42 + 19x + 2x2 = 36 + 12x + x2

Solving for variable 'x'.

Reorder the terms:
42 + -36 + 19x + -12x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 42 + -36 = 6
6 + 19x + -12x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 19x + -12x = 7x
6 + 7x + 2x2 + -1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
6 + 7x + 1x2 = 36 + 12x + x2 + -36 + -12x + -1x2

Reorder the terms:
6 + 7x + 1x2 = 36 + -36 + 12x + -12x + x2 + -1x2

Combine like terms: 36 + -36 = 0
6 + 7x + 1x2 = 0 + 12x + -12x + x2 + -1x2
6 + 7x + 1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
6 + 7x + 1x2 = 0 + x2 + -1x2
6 + 7x + 1x2 = x2 + -1x2

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

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

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

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-6, -1}