(4x-12)(7x+28)=0

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Solution for (4x-12)(7x+28)=0 equation: 


Simplifying
(4x + -12)(7x + 28) = 0

Reorder the terms:
(-12 + 4x)(7x + 28) = 0

Reorder the terms:
(-12 + 4x)(28 + 7x) = 0

Multiply (-12 + 4x) * (28 + 7x)
(-12(28 + 7x) + 4x * (28 + 7x)) = 0
((28 * -12 + 7x * -12) + 4x * (28 + 7x)) = 0
((-336 + -84x) + 4x * (28 + 7x)) = 0
(-336 + -84x + (28 * 4x + 7x * 4x)) = 0
(-336 + -84x + (112x + 28x2)) = 0

Combine like terms: -84x + 112x = 28x
(-336 + 28x + 28x2) = 0

Solving
-336 + 28x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '28'.
28(-12 + x + x2) = 0

Factor a trinomial.
28((-4 + -1x)(3 + -1x)) = 0

Ignore the factor 28.

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 3}

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