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

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


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

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

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

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

Combine like terms: 5x + 28x = 33x
(35 + 33x + 4x2) = 0

Solving
35 + 33x + 4x2 = 0

Solving for variable 'x'.

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


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

Simplifying
7 + x = 0

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

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

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

Simplifying
x = -7

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

Simplifying
5 + 4x = 0

Solving
5 + 4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4x = 0 + -5

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

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

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25
Solution
x = {-7, -1.25}

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