(3x-4)(7x-21)=0

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Solution for (3x-4)(7x-21)=0 equation: 


Simplifying
(3x + -4)(7x + -21) = 0

Reorder the terms:
(-4 + 3x)(7x + -21) = 0

Reorder the terms:
(-4 + 3x)(-21 + 7x) = 0

Multiply (-4 + 3x) * (-21 + 7x)
(-4(-21 + 7x) + 3x * (-21 + 7x)) = 0
((-21 * -4 + 7x * -4) + 3x * (-21 + 7x)) = 0
((84 + -28x) + 3x * (-21 + 7x)) = 0
(84 + -28x + (-21 * 3x + 7x * 3x)) = 0
(84 + -28x + (-63x + 21x2)) = 0

Combine like terms: -28x + -63x = -91x
(84 + -91x + 21x2) = 0

Solving
84 + -91x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(12 + -13x + 3x2) = 0

Factor a trinomial.
7((4 + -3x)(3 + -1x)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1.333333333, 3}

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