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

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


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

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

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

Multiply (12 + 4x) * (-4 + 7x)
(12(-4 + 7x) + 4x * (-4 + 7x)) = 0
((-4 * 12 + 7x * 12) + 4x * (-4 + 7x)) = 0
((-48 + 84x) + 4x * (-4 + 7x)) = 0
(-48 + 84x + (-4 * 4x + 7x * 4x)) = 0
(-48 + 84x + (-16x + 28x2)) = 0

Combine like terms: 84x + -16x = 68x
(-48 + 68x + 28x2) = 0

Solving
-48 + 68x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + 17x + 7x2) = 0

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

Ignore the factor 4.

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 '(4 + -7x)' equal to zero and attempt to solve:

Simplifying
4 + -7x = 0

Solving
4 + -7x = 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 + -7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7x = 0 + -4
-7x = 0 + -4

Combine like terms: 0 + -4 = -4
-7x = -4

Divide each side by '-7'.
x = 0.5714285714

Simplifying
x = 0.5714285714
Solution
x = {-3, 0.5714285714}

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