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

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


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

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

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

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

Combine like terms: 7x + 20x = 27x
(28 + 27x + 5x2) = 0

Solving
28 + 27x + 5x2 = 0

Solving for variable 'x'.

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


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

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4

Subproblem 2
Set the factor '(7 + 5x)' equal to zero and attempt to solve:

Simplifying
7 + 5x = 0

Solving
7 + 5x = 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 + 5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5x = 0 + -7
5x = 0 + -7

Combine like terms: 0 + -7 = -7
5x = -7

Divide each side by '5'.
x = -1.4

Simplifying
x = -1.4
Solution
x = {-4, -1.4}

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