(3x+7)(1-4x)=0

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Solution for (3x+7)(1-4x)=0 equation: 


Simplifying
(3x + 7)(1 + -4x) = 0

Reorder the terms:
(7 + 3x)(1 + -4x) = 0

Multiply (7 + 3x) * (1 + -4x)
(7(1 + -4x) + 3x * (1 + -4x)) = 0
((1 * 7 + -4x * 7) + 3x * (1 + -4x)) = 0
((7 + -28x) + 3x * (1 + -4x)) = 0
(7 + -28x + (1 * 3x + -4x * 3x)) = 0
(7 + -28x + (3x + -12x2)) = 0

Combine like terms: -28x + 3x = -25x
(7 + -25x + -12x2) = 0

Solving
7 + -25x + -12x2 = 0

Solving for variable 'x'.

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


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 + 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 = {0.25, -2.333333333}

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