(7x+4)(-5x-8)=0

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Solution for (7x+4)(-5x-8)=0 equation: 


Simplifying
(7x + 4)(-5x + -8) = 0

Reorder the terms:
(4 + 7x)(-5x + -8) = 0

Reorder the terms:
(4 + 7x)(-8 + -5x) = 0

Multiply (4 + 7x) * (-8 + -5x)
(4(-8 + -5x) + 7x * (-8 + -5x)) = 0
((-8 * 4 + -5x * 4) + 7x * (-8 + -5x)) = 0
((-32 + -20x) + 7x * (-8 + -5x)) = 0
(-32 + -20x + (-8 * 7x + -5x * 7x)) = 0
(-32 + -20x + (-56x + -35x2)) = 0

Combine like terms: -20x + -56x = -76x
(-32 + -76x + -35x2) = 0

Solving
-32 + -76x + -35x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(32 + 76x + 35x2) = 0

Factor a trinomial.
-1((8 + 5x)(4 + 7x)) = 0

Ignore the factor -1.

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 '(4 + 7x)' equal to zero and attempt to solve:

Simplifying
4 + 7x = 0

Solving
4 + 7x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7x = 0 + -4
7x = 0 + -4

Combine like terms: 0 + -4 = -4
7x = -4

Divide each side by '7'.
x = -0.5714285714

Simplifying
x = -0.5714285714
Solution
x = {-1.6, -0.5714285714}

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