(3x-8)(7x-15)=0

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Solution for (3x-8)(7x-15)=0 equation: 


Simplifying
(3x + -8)(7x + -15) = 0

Reorder the terms:
(-8 + 3x)(7x + -15) = 0

Reorder the terms:
(-8 + 3x)(-15 + 7x) = 0

Multiply (-8 + 3x) * (-15 + 7x)
(-8(-15 + 7x) + 3x * (-15 + 7x)) = 0
((-15 * -8 + 7x * -8) + 3x * (-15 + 7x)) = 0
((120 + -56x) + 3x * (-15 + 7x)) = 0
(120 + -56x + (-15 * 3x + 7x * 3x)) = 0
(120 + -56x + (-45x + 21x2)) = 0

Combine like terms: -56x + -45x = -101x
(120 + -101x + 21x2) = 0

Solving
120 + -101x + 21x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(15 + -7x)(8 + -3x) = 0


Subproblem 1
Set the factor '(15 + -7x)' equal to zero and attempt to solve:

Simplifying
15 + -7x = 0

Solving
15 + -7x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -7x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -7x = 0 + -15
-7x = 0 + -15

Combine like terms: 0 + -15 = -15
-7x = -15

Divide each side by '-7'.
x = 2.142857143

Simplifying
x = 2.142857143

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 = {2.142857143, 2.666666667}

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