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

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


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

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

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

Multiply (-7 + 3x) * (8 + 5x)
(-7(8 + 5x) + 3x * (8 + 5x)) = 0
((8 * -7 + 5x * -7) + 3x * (8 + 5x)) = 0
((-56 + -35x) + 3x * (8 + 5x)) = 0
(-56 + -35x + (8 * 3x + 5x * 3x)) = 0
(-56 + -35x + (24x + 15x2)) = 0

Combine like terms: -35x + 24x = -11x
(-56 + -11x + 15x2) = 0

Solving
-56 + -11x + 15x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-8 + -5x)' equal to zero and attempt to solve:

Simplifying
-8 + -5x = 0

Solving
-8 + -5x = 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 + -5x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5x = 0 + 8
-5x = 0 + 8

Combine like terms: 0 + 8 = 8
-5x = 8

Divide each side by '-5'.
x = -1.6

Simplifying
x = -1.6

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

Simplifying
7 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-1.6, 2.333333333}

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