(7+x)(3x+8)=0

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Solution for (7+x)(3x+8)=0 equation: 


Simplifying
(7 + x)(3x + 8) = 0

Reorder the terms:
(7 + x)(8 + 3x) = 0

Multiply (7 + x) * (8 + 3x)
(7(8 + 3x) + x(8 + 3x)) = 0
((8 * 7 + 3x * 7) + x(8 + 3x)) = 0
((56 + 21x) + x(8 + 3x)) = 0
(56 + 21x + (8 * x + 3x * x)) = 0
(56 + 21x + (8x + 3x2)) = 0

Combine like terms: 21x + 8x = 29x
(56 + 29x + 3x2) = 0

Solving
56 + 29x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + x)(8 + 3x) = 0


Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

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

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

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

Simplifying
x = -7

Subproblem 2
Set the factor '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Divide each side by '3'.
x = -2.666666667

Simplifying
x = -2.666666667
Solution
x = {-7, -2.666666667}

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