(4x-8)(7x+21)=0

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Solution for (4x-8)(7x+21)=0 equation: 


Simplifying
(4x + -8)(7x + 21) = 0

Reorder the terms:
(-8 + 4x)(7x + 21) = 0

Reorder the terms:
(-8 + 4x)(21 + 7x) = 0

Multiply (-8 + 4x) * (21 + 7x)
(-8(21 + 7x) + 4x * (21 + 7x)) = 0
((21 * -8 + 7x * -8) + 4x * (21 + 7x)) = 0
((-168 + -56x) + 4x * (21 + 7x)) = 0
(-168 + -56x + (21 * 4x + 7x * 4x)) = 0
(-168 + -56x + (84x + 28x2)) = 0

Combine like terms: -56x + 84x = 28x
(-168 + 28x + 28x2) = 0

Solving
-168 + 28x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '28'.
28(-6 + x + x2) = 0

Factor a trinomial.
28((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 28.

Subproblem 1
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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}

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