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

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


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

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

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

Multiply (5 + 4x) * (3 + 7x)
(5(3 + 7x) + 4x * (3 + 7x)) = 0
((3 * 5 + 7x * 5) + 4x * (3 + 7x)) = 0
((15 + 35x) + 4x * (3 + 7x)) = 0
(15 + 35x + (3 * 4x + 7x * 4x)) = 0
(15 + 35x + (12x + 28x2)) = 0

Combine like terms: 35x + 12x = 47x
(15 + 47x + 28x2) = 0

Solving
15 + 47x + 28x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(3 + 7x)' equal to zero and attempt to solve:

Simplifying
3 + 7x = 0

Solving
3 + 7x = 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 + 7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7x = 0 + -3
7x = 0 + -3

Combine like terms: 0 + -3 = -3
7x = -3

Divide each side by '7'.
x = -0.4285714286

Simplifying
x = -0.4285714286
Solution
x = {-1.25, -0.4285714286}

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