(4x+1)(7-2x)=0

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Solution for (4x+1)(7-2x)=0 equation: 


Simplifying
(4x + 1)(7 + -2x) = 0

Reorder the terms:
(1 + 4x)(7 + -2x) = 0

Multiply (1 + 4x) * (7 + -2x)
(1(7 + -2x) + 4x * (7 + -2x)) = 0
((7 * 1 + -2x * 1) + 4x * (7 + -2x)) = 0
((7 + -2x) + 4x * (7 + -2x)) = 0
(7 + -2x + (7 * 4x + -2x * 4x)) = 0
(7 + -2x + (28x + -8x2)) = 0

Combine like terms: -2x + 28x = 26x
(7 + 26x + -8x2) = 0

Solving
7 + 26x + -8x2 = 0

Solving for variable 'x'.

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


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

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5

Subproblem 2
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
Solution
x = {3.5, -0.25}

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