2(6x+7)(7x-4)=0

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Solution for 2(6x+7)(7x-4)=0 equation: 


Simplifying
2(6x + 7)(7x + -4) = 0

Reorder the terms:
2(7 + 6x)(7x + -4) = 0

Reorder the terms:
2(7 + 6x)(-4 + 7x) = 0

Multiply (7 + 6x) * (-4 + 7x)
2(7(-4 + 7x) + 6x * (-4 + 7x)) = 0
2((-4 * 7 + 7x * 7) + 6x * (-4 + 7x)) = 0
2((-28 + 49x) + 6x * (-4 + 7x)) = 0
2(-28 + 49x + (-4 * 6x + 7x * 6x)) = 0
2(-28 + 49x + (-24x + 42x2)) = 0

Combine like terms: 49x + -24x = 25x
2(-28 + 25x + 42x2) = 0
(-28 * 2 + 25x * 2 + 42x2 * 2) = 0
(-56 + 50x + 84x2) = 0

Solving
-56 + 50x + 84x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 25x + 42x2) = 0

Factor a trinomial.
2((-7 + -6x)(4 + -7x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -6x)' equal to zero and attempt to solve:

Simplifying
-7 + -6x = 0

Solving
-7 + -6x = 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 + -6x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6x = 0 + 7
-6x = 0 + 7

Combine like terms: 0 + 7 = 7
-6x = 7

Divide each side by '-6'.
x = -1.166666667

Simplifying
x = -1.166666667

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 = {-1.166666667, 0.5714285714}

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