(7x+4)(-5x-8)=9

Solution for (7x+4)(-5x-8)=9 equation:

Simplifying
(7x + 4)(-5x + -8) = 9

Reorder the terms:
(4 + 7x)(-5x + -8) = 9

Reorder the terms:
(4 + 7x)(-8 + -5x) = 9

Multiply (4 + 7x) * (-8 + -5x)
(4(-8 + -5x) + 7x * (-8 + -5x)) = 9
((-8 * 4 + -5x * 4) + 7x * (-8 + -5x)) = 9
((-32 + -20x) + 7x * (-8 + -5x)) = 9
(-32 + -20x + (-8 * 7x + -5x * 7x)) = 9
(-32 + -20x + (-56x + -35x2)) = 9

Combine like terms: -20x + -56x = -76x
(-32 + -76x + -35x2) = 9

Solving
-32 + -76x + -35x2 = 9

Solving for variable 'x'.

Reorder the terms:
-32 + -9 + -76x + -35x2 = 9 + -9

Combine like terms: -32 + -9 = -41
-41 + -76x + -35x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-41 + -76x + -35x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(41 + 76x + 35x2) = 0

Factor a trinomial.
-1((41 + 35x)(1 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(41 + 35x)' equal to zero and attempt to solve:

Simplifying
41 + 35x = 0

Solving
41 + 35x = 0

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

Add '-41' to each side of the equation.
41 + -41 + 35x = 0 + -41

Combine like terms: 41 + -41 = 0
0 + 35x = 0 + -41
35x = 0 + -41

Combine like terms: 0 + -41 = -41
35x = -41

Divide each side by '35'.
x = -1.171428571

Simplifying
x = -1.171428571
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 = {-1.171428571, -1}