(3x+8)(5x+7)=0

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Solution for (3x+8)(5x+7)=0 equation: 


Simplifying
(3x + 8)(5x + 7) = 0

Reorder the terms:
(8 + 3x)(5x + 7) = 0

Reorder the terms:
(8 + 3x)(7 + 5x) = 0

Multiply (8 + 3x) * (7 + 5x)
(8(7 + 5x) + 3x * (7 + 5x)) = 0
((7 * 8 + 5x * 8) + 3x * (7 + 5x)) = 0
((56 + 40x) + 3x * (7 + 5x)) = 0
(56 + 40x + (7 * 3x + 5x * 3x)) = 0
(56 + 40x + (21x + 15x2)) = 0

Combine like terms: 40x + 21x = 61x
(56 + 61x + 15x2) = 0

Solving
56 + 61x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + 3x)(7 + 5x) = 0


Subproblem 1
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

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 = {-2.666666667, -1.4}

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