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

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


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

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

Multiply (3 + x) * (7 + 5x)
(3(7 + 5x) + x(7 + 5x)) = 0
((7 * 3 + 5x * 3) + x(7 + 5x)) = 0
((21 + 15x) + x(7 + 5x)) = 0
(21 + 15x + (7 * x + 5x * x)) = 0
(21 + 15x + (7x + 5x2)) = 0

Combine like terms: 15x + 7x = 22x
(21 + 22x + 5x2) = 0

Solving
21 + 22x + 5x2 = 0

Solving for variable 'x'.

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


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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3

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 = {-3, -1.4}

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