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

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


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

Reorder the terms:
(1 + 4x)(2x + -7) = 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.
(-1 + -4x)(7 + -2x) = 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 + -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
Solution
x = {-0.25, 3.5}

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