(x+7)(2x+5)=-7

Solution for (x+7)(2x+5)=-7 equation:

Simplifying
(x + 7)(2x + 5) = -7

Reorder the terms:
(7 + x)(2x + 5) = -7

Reorder the terms:
(7 + x)(5 + 2x) = -7

Multiply (7 + x) * (5 + 2x)
(7(5 + 2x) + x(5 + 2x)) = -7
((5 * 7 + 2x * 7) + x(5 + 2x)) = -7
((35 + 14x) + x(5 + 2x)) = -7
(35 + 14x + (5 * x + 2x * x)) = -7
(35 + 14x + (5x + 2x2)) = -7

Combine like terms: 14x + 5x = 19x
(35 + 19x + 2x2) = -7

Solving
35 + 19x + 2x2 = -7

Solving for variable 'x'.

Reorder the terms:
35 + 7 + 19x + 2x2 = -7 + 7

Combine like terms: 35 + 7 = 42
42 + 19x + 2x2 = -7 + 7

Combine like terms: -7 + 7 = 0
42 + 19x + 2x2 = 0

Factor a trinomial.
(6 + x)(7 + 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 '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

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

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

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

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
Solution
x = {-6, -3.5}