(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 = -35x
(-84 + -35x + 21x2) = 0

Solving
-84 + -35x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-12 + -5x + 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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