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

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


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

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

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

Combine like terms: -7x + 8x = 1x
(28 + 1x + -2x2) = 0

Solving
28 + 1x + -2x2 = 0

Solving for variable 'x'.

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


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

Simplifying
4 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {4, -3.5}

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