2(7x-4)(3x+4)=0

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Solution for 2(7x-4)(3x+4)=0 equation: 


Simplifying
2(7x + -4)(3x + 4) = 0

Reorder the terms:
2(-4 + 7x)(3x + 4) = 0

Reorder the terms:
2(-4 + 7x)(4 + 3x) = 0

Multiply (-4 + 7x) * (4 + 3x)
2(-4(4 + 3x) + 7x * (4 + 3x)) = 0
2((4 * -4 + 3x * -4) + 7x * (4 + 3x)) = 0
2((-16 + -12x) + 7x * (4 + 3x)) = 0
2(-16 + -12x + (4 * 7x + 3x * 7x)) = 0
2(-16 + -12x + (28x + 21x2)) = 0

Combine like terms: -12x + 28x = 16x
2(-16 + 16x + 21x2) = 0
(-16 * 2 + 16x * 2 + 21x2 * 2) = 0
(-32 + 32x + 42x2) = 0

Solving
-32 + 32x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 16x + 21x2) = 0

Factor a trinomial.
2((-4 + -3x)(4 + -7x)) = 0

Ignore the factor 2.

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 '(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 = {-1.333333333, 0.5714285714}

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