(4x-12)(7x+16)=0

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Solution for (4x-12)(7x+16)=0 equation: 


Simplifying
(4x + -12)(7x + 16) = 0

Reorder the terms:
(-12 + 4x)(7x + 16) = 0

Reorder the terms:
(-12 + 4x)(16 + 7x) = 0

Multiply (-12 + 4x) * (16 + 7x)
(-12(16 + 7x) + 4x * (16 + 7x)) = 0
((16 * -12 + 7x * -12) + 4x * (16 + 7x)) = 0
((-192 + -84x) + 4x * (16 + 7x)) = 0
(-192 + -84x + (16 * 4x + 7x * 4x)) = 0
(-192 + -84x + (64x + 28x2)) = 0

Combine like terms: -84x + 64x = -20x
(-192 + -20x + 28x2) = 0

Solving
-192 + -20x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-48 + -5x + 7x2) = 0

Factor a trinomial.
4((-16 + -7x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-16 + -7x)' equal to zero and attempt to solve:

Simplifying
-16 + -7x = 0

Solving
-16 + -7x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -7x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -7x = 0 + 16
-7x = 0 + 16

Combine like terms: 0 + 16 = 16
-7x = 16

Divide each side by '-7'.
x = -2.285714286

Simplifying
x = -2.285714286

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 = {-2.285714286, 3}

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