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

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


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

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

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

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

Combine like terms: -4x + -42x = -46x
(28 + -46x + 6x2) = 0

Solving
28 + -46x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + -23x + 3x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {0.6666666667, 7}

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