6(7-10x)(1-4x)=0

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Solution for 6(7-10x)(1-4x)=0 equation: 


Simplifying
6(7 + -10x)(1 + -4x) = 0

Multiply (7 + -10x) * (1 + -4x)
6(7(1 + -4x) + -10x * (1 + -4x)) = 0
6((1 * 7 + -4x * 7) + -10x * (1 + -4x)) = 0
6((7 + -28x) + -10x * (1 + -4x)) = 0
6(7 + -28x + (1 * -10x + -4x * -10x)) = 0
6(7 + -28x + (-10x + 40x2)) = 0

Combine like terms: -28x + -10x = -38x
6(7 + -38x + 40x2) = 0
(7 * 6 + -38x * 6 + 40x2 * 6) = 0
(42 + -228x + 240x2) = 0

Solving
42 + -228x + 240x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(7 + -38x + 40x2) = 0

Factor a trinomial.
6((1 + -4x)(7 + -10x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
Set the factor '(7 + -10x)' equal to zero and attempt to solve:

Simplifying
7 + -10x = 0

Solving
7 + -10x = 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 + -10x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -10x = 0 + -7
-10x = 0 + -7

Combine like terms: 0 + -7 = -7
-10x = -7

Divide each side by '-10'.
x = 0.7

Simplifying
x = 0.7
Solution
x = {0.25, 0.7}

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