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

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


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

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

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

Multiply (7 + 4x) * (-4 + -5x)
(7(-4 + -5x) + 4x * (-4 + -5x)) = 0
((-4 * 7 + -5x * 7) + 4x * (-4 + -5x)) = 0
((-28 + -35x) + 4x * (-4 + -5x)) = 0
(-28 + -35x + (-4 * 4x + -5x * 4x)) = 0
(-28 + -35x + (-16x + -20x2)) = 0

Combine like terms: -35x + -16x = -51x
(-28 + -51x + -20x2) = 0

Solving
-28 + -51x + -20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(28 + 51x + 20x2) = 0

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

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + 4x)' equal to zero and attempt to solve:

Simplifying
7 + 4x = 0

Solving
7 + 4x = 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 + 4x = 0 + -7

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

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

Divide each side by '4'.
x = -1.75

Simplifying
x = -1.75

Subproblem 2
Set the factor '(4 + 5x)' equal to zero and attempt to solve:

Simplifying
4 + 5x = 0

Solving
4 + 5x = 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 + 5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5x = 0 + -4
5x = 0 + -4

Combine like terms: 0 + -4 = -4
5x = -4

Divide each side by '5'.
x = -0.8

Simplifying
x = -0.8
Solution
x = {-1.75, -0.8}

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