(5x+3)(7x+4)=0

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Solution for (5x+3)(7x+4)=0 equation: 


Simplifying
(5x + 3)(7x + 4) = 0

Reorder the terms:
(3 + 5x)(7x + 4) = 0

Reorder the terms:
(3 + 5x)(4 + 7x) = 0

Multiply (3 + 5x) * (4 + 7x)
(3(4 + 7x) + 5x * (4 + 7x)) = 0
((4 * 3 + 7x * 3) + 5x * (4 + 7x)) = 0
((12 + 21x) + 5x * (4 + 7x)) = 0
(12 + 21x + (4 * 5x + 7x * 5x)) = 0
(12 + 21x + (20x + 35x2)) = 0

Combine like terms: 21x + 20x = 41x
(12 + 41x + 35x2) = 0

Solving
12 + 41x + 35x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + 5x)(4 + 7x) = 0


Subproblem 1
Set the factor '(3 + 5x)' equal to zero and attempt to solve:

Simplifying
3 + 5x = 0

Solving
3 + 5x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5x = 0 + -3
5x = 0 + -3

Combine like terms: 0 + -3 = -3
5x = -3

Divide each side by '5'.
x = -0.6

Simplifying
x = -0.6

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 = {-0.6, -0.5714285714}

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