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

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


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

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

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

Multiply (-7 + 4x) * (7 + 3x)
2(-7(7 + 3x) + 4x * (7 + 3x)) = 0
2((7 * -7 + 3x * -7) + 4x * (7 + 3x)) = 0
2((-49 + -21x) + 4x * (7 + 3x)) = 0
2(-49 + -21x + (7 * 4x + 3x * 4x)) = 0
2(-49 + -21x + (28x + 12x2)) = 0

Combine like terms: -21x + 28x = 7x
2(-49 + 7x + 12x2) = 0
(-49 * 2 + 7x * 2 + 12x2 * 2) = 0
(-98 + 14x + 24x2) = 0

Solving
-98 + 14x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-49 + 7x + 12x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve:

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x = 0 + 7
-3x = 0 + 7

Combine like terms: 0 + 7 = 7
-3x = 7

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333

Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4x = 0 + -7

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

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

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {-2.333333333, 1.75}

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