(4x+7)(8-x)=0

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Solution for (4x+7)(8-x)=0 equation: 


Simplifying
(4x + 7)(8 + -1x) = 0

Reorder the terms:
(7 + 4x)(8 + -1x) = 0

Multiply (7 + 4x) * (8 + -1x)
(7(8 + -1x) + 4x * (8 + -1x)) = 0
((8 * 7 + -1x * 7) + 4x * (8 + -1x)) = 0
((56 + -7x) + 4x * (8 + -1x)) = 0
(56 + -7x + (8 * 4x + -1x * 4x)) = 0
(56 + -7x + (32x + -4x2)) = 0

Combine like terms: -7x + 32x = 25x
(56 + 25x + -4x2) = 0

Solving
56 + 25x + -4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + -1x)(7 + 4x) = 0


Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(7 + 4x)' equal to zero and attempt to solve:

Simplifying
7 + 4x = 0

Solving
7 + 4x = 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 + 4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4x = 0 + -7
4x = 0 + -7

Combine like terms: 0 + -7 = -7
4x = -7

Divide each side by '4'.
x = -1.75

Simplifying
x = -1.75
Solution
x = {8, -1.75}

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