(x+3)(5x-2)=-14

Solution for (x+3)(5x-2)=-14 equation:

Simplifying
(x + 3)(5x + -2) = -14

Reorder the terms:
(3 + x)(5x + -2) = -14

Reorder the terms:
(3 + x)(-2 + 5x) = -14

Multiply (3 + x) * (-2 + 5x)
(3(-2 + 5x) + x(-2 + 5x)) = -14
((-2 * 3 + 5x * 3) + x(-2 + 5x)) = -14
((-6 + 15x) + x(-2 + 5x)) = -14
(-6 + 15x + (-2 * x + 5x * x)) = -14
(-6 + 15x + (-2x + 5x2)) = -14

Combine like terms: 15x + -2x = 13x
(-6 + 13x + 5x2) = -14

Solving
-6 + 13x + 5x2 = -14

Solving for variable 'x'.

Reorder the terms:
-6 + 14 + 13x + 5x2 = -14 + 14

Combine like terms: -6 + 14 = 8
8 + 13x + 5x2 = -14 + 14

Combine like terms: -14 + 14 = 0
8 + 13x + 5x2 = 0

Factor a trinomial.
(8 + 5x)(1 + x) = 0

Subproblem 1
Set the factor '(8 + 5x)' equal to zero and attempt to solve:

Simplifying
8 + 5x = 0

Solving
8 + 5x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5x = 0 + -8
5x = 0 + -8

Combine like terms: 0 + -8 = -8
5x = -8

Divide each side by '5'.
x = -1.6

Simplifying
x = -1.6
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 = {-1.6, -1}