(42x-7)(20-5x-3)=0

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Solution for (42x-7)(20-5x-3)=0 equation: 


Simplifying
(42x + -7)(20 + -5x + -3) = 0

Reorder the terms:
(-7 + 42x)(20 + -5x + -3) = 0

Reorder the terms:
(-7 + 42x)(20 + -3 + -5x) = 0

Combine like terms: 20 + -3 = 17
(-7 + 42x)(17 + -5x) = 0

Multiply (-7 + 42x) * (17 + -5x)
(-7(17 + -5x) + 42x * (17 + -5x)) = 0
((17 * -7 + -5x * -7) + 42x * (17 + -5x)) = 0
((-119 + 35x) + 42x * (17 + -5x)) = 0
(-119 + 35x + (17 * 42x + -5x * 42x)) = 0
(-119 + 35x + (714x + -210x2)) = 0

Combine like terms: 35x + 714x = 749x
(-119 + 749x + -210x2) = 0

Solving
-119 + 749x + -210x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-17 + 107x + -30x2) = 0

Factor a trinomial.
7((-17 + 5x)(1 + -6x)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-17 + 5x)' equal to zero and attempt to solve:

Simplifying
-17 + 5x = 0

Solving
-17 + 5x = 0

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

Add '17' to each side of the equation.
-17 + 17 + 5x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 5x = 0 + 17
5x = 0 + 17

Combine like terms: 0 + 17 = 17
5x = 17

Divide each side by '5'.
x = 3.4

Simplifying
x = 3.4

Subproblem 2
Set the factor '(1 + -6x)' equal to zero and attempt to solve:

Simplifying
1 + -6x = 0

Solving
1 + -6x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6x = 0 + -1
-6x = 0 + -1

Combine like terms: 0 + -1 = -1
-6x = -1

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667
Solution
x = {3.4, 0.1666666667}

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