2x^2+15x+7=2x+1

Solution for 2x^2+15x+7=2x+1 equation:

Simplifying
2x2 + 15x + 7 = 2x + 1

Reorder the terms:
7 + 15x + 2x2 = 2x + 1

Reorder the terms:
7 + 15x + 2x2 = 1 + 2x

Solving
7 + 15x + 2x2 = 1 + 2x

Solving for variable 'x'.

Reorder the terms:
7 + -1 + 15x + -2x + 2x2 = 1 + 2x + -1 + -2x

Combine like terms: 7 + -1 = 6
6 + 15x + -2x + 2x2 = 1 + 2x + -1 + -2x

Combine like terms: 15x + -2x = 13x
6 + 13x + 2x2 = 1 + 2x + -1 + -2x

Reorder the terms:
6 + 13x + 2x2 = 1 + -1 + 2x + -2x

Combine like terms: 1 + -1 = 0
6 + 13x + 2x2 = 0 + 2x + -2x
6 + 13x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
6 + 13x + 2x2 = 0

Factor a trinomial.
(6 + x)(1 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-6, -0.5}