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

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


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

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

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

Multiply (5 + 3x) * (3 + x)
(5(3 + x) + 3x * (3 + x)) = 7
((3 * 5 + x * 5) + 3x * (3 + x)) = 7
((15 + 5x) + 3x * (3 + x)) = 7
(15 + 5x + (3 * 3x + x * 3x)) = 7
(15 + 5x + (9x + 3x2)) = 7

Combine like terms: 5x + 9x = 14x
(15 + 14x + 3x2) = 7

Solving
15 + 14x + 3x2 = 7

Solving for variable 'x'.

Reorder the terms:
15 + -7 + 14x + 3x2 = 7 + -7

Combine like terms: 15 + -7 = 8
8 + 14x + 3x2 = 7 + -7

Combine like terms: 7 + -7 = 0
8 + 14x + 3x2 = 0

Factor a trinomial.
(4 + x)(2 + 3x) = 0


Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-4, -0.6666666667}

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