(3x-7)(4x-8)=0

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Solution for (3x-7)(4x-8)=0 equation: 


Simplifying
(3x + -7)(4x + -8) = 0

Reorder the terms:
(-7 + 3x)(4x + -8) = 0

Reorder the terms:
(-7 + 3x)(-8 + 4x) = 0

Multiply (-7 + 3x) * (-8 + 4x)
(-7(-8 + 4x) + 3x * (-8 + 4x)) = 0
((-8 * -7 + 4x * -7) + 3x * (-8 + 4x)) = 0
((56 + -28x) + 3x * (-8 + 4x)) = 0
(56 + -28x + (-8 * 3x + 4x * 3x)) = 0
(56 + -28x + (-24x + 12x2)) = 0

Combine like terms: -28x + -24x = -52x
(56 + -52x + 12x2) = 0

Solving
56 + -52x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(14 + -13x + 3x2) = 0

Factor a trinomial.
4((2 + -1x)(7 + -3x)) = 0

Ignore the factor 4.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
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
Solution
x = {2, 2.333333333}

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