(14x+3)(x+1)=-(2x+3)

Solution for (14x+3)(x+1)=-(2x+3) equation:

Simplifying
(14x + 3)(x + 1) = -1(2x + 3)

Reorder the terms:
(3 + 14x)(x + 1) = -1(2x + 3)

Reorder the terms:
(3 + 14x)(1 + x) = -1(2x + 3)

Multiply (3 + 14x) * (1 + x)
(3(1 + x) + 14x * (1 + x)) = -1(2x + 3)
((1 * 3 + x * 3) + 14x * (1 + x)) = -1(2x + 3)
((3 + 3x) + 14x * (1 + x)) = -1(2x + 3)
(3 + 3x + (1 * 14x + x * 14x)) = -1(2x + 3)
(3 + 3x + (14x + 14x2)) = -1(2x + 3)

Combine like terms: 3x + 14x = 17x
(3 + 17x + 14x2) = -1(2x + 3)

Reorder the terms:
3 + 17x + 14x2 = -1(3 + 2x)
3 + 17x + 14x2 = (3 * -1 + 2x * -1)
3 + 17x + 14x2 = (-3 + -2x)

Solving
3 + 17x + 14x2 = -3 + -2x

Solving for variable 'x'.

Reorder the terms:
3 + 3 + 17x + 2x + 14x2 = -3 + -2x + 3 + 2x

Combine like terms: 3 + 3 = 6
6 + 17x + 2x + 14x2 = -3 + -2x + 3 + 2x

Combine like terms: 17x + 2x = 19x
6 + 19x + 14x2 = -3 + -2x + 3 + 2x

Reorder the terms:
6 + 19x + 14x2 = -3 + 3 + -2x + 2x

Combine like terms: -3 + 3 = 0
6 + 19x + 14x2 = 0 + -2x + 2x
6 + 19x + 14x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
6 + 19x + 14x2 = 0

Factor a trinomial.
(6 + 7x)(1 + 2x) = 0

Subproblem 1
Set the factor '(6 + 7x)' equal to zero and attempt to solve:

Simplifying
6 + 7x = 0

Solving
6 + 7x = 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 + 7x = 0 + -6

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

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

Divide each side by '7'.
x = -0.8571428571

Simplifying
x = -0.8571428571
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 = {-0.8571428571, -0.5}