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

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


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

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

Multiply (-4 + 3x) * (7 + -2x)
2(-4(7 + -2x) + 3x * (7 + -2x)) = 0
2((7 * -4 + -2x * -4) + 3x * (7 + -2x)) = 0
2((-28 + 8x) + 3x * (7 + -2x)) = 0
2(-28 + 8x + (7 * 3x + -2x * 3x)) = 0
2(-28 + 8x + (21x + -6x2)) = 0

Combine like terms: 8x + 21x = 29x
2(-28 + 29x + -6x2) = 0
(-28 * 2 + 29x * 2 + -6x2 * 2) = 0
(-56 + 58x + -12x2) = 0

Solving
-56 + 58x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 29x + -6x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 2x)' equal to zero and attempt to solve:

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 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 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Divide each side by '2'.
x = 3.5

Simplifying
x = 3.5

Subproblem 2
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
Solution
x = {3.5, 1.333333333}

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