(x+3)(-2x-7)=

Solution for (x+3)(-2x-7)= equation:

Simplifying
(x + 3)(-2x + -7) = 0

Reorder the terms:
(3 + x)(-2x + -7) = 0

Reorder the terms:
(3 + x)(-7 + -2x) = 0

Multiply (3 + x) * (-7 + -2x)
(3(-7 + -2x) + x(-7 + -2x)) = 0
((-7 * 3 + -2x * 3) + x(-7 + -2x)) = 0
((-21 + -6x) + x(-7 + -2x)) = 0
(-21 + -6x + (-7 * x + -2x * x)) = 0
(-21 + -6x + (-7x + -2x2)) = 0

Combine like terms: -6x + -7x = -13x
(-21 + -13x + -2x2) = 0

Solving
-21 + -13x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 13x + 2x2) = 0

Factor a trinomial.
-1((7 + 2x)(3 + x)) = 0

Ignore the factor -1.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-3.5, -3}