(-6x+1)(7x-4)=0

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Solution for (-6x+1)(7x-4)=0 equation: 


Simplifying
(-6x + 1)(7x + -4) = 0

Reorder the terms:
(1 + -6x)(7x + -4) = 0

Reorder the terms:
(1 + -6x)(-4 + 7x) = 0

Multiply (1 + -6x) * (-4 + 7x)
(1(-4 + 7x) + -6x * (-4 + 7x)) = 0
((-4 * 1 + 7x * 1) + -6x * (-4 + 7x)) = 0
((-4 + 7x) + -6x * (-4 + 7x)) = 0
(-4 + 7x + (-4 * -6x + 7x * -6x)) = 0
(-4 + 7x + (24x + -42x2)) = 0

Combine like terms: 7x + 24x = 31x
(-4 + 31x + -42x2) = 0

Solving
-4 + 31x + -42x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + 7x)(1 + -6x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(1 + -6x)' equal to zero and attempt to solve:

Simplifying
1 + -6x = 0

Solving
1 + -6x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6x = 0 + -1
-6x = 0 + -1

Combine like terms: 0 + -1 = -1
-6x = -1

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667
Solution
x = {0.5714285714, 0.1666666667}

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