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

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


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

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

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

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

Combine like terms: 12x + 35x = 47x
(21 + 47x + 20x2) = 0

Solving
21 + 47x + 20x2 = 0

Solving for variable 'x'.

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


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 '(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
Solution
x = {-1.75, -0.6}

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