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

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


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

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

Multiply (7 + 4x) * (2 + x)
(7(2 + x) + 4x * (2 + x)) = 0
((2 * 7 + x * 7) + 4x * (2 + x)) = 0
((14 + 7x) + 4x * (2 + x)) = 0
(14 + 7x + (2 * 4x + x * 4x)) = 0
(14 + 7x + (8x + 4x2)) = 0

Combine like terms: 7x + 8x = 15x
(14 + 15x + 4x2) = 0

Solving
14 + 15x + 4x2 = 0

Solving for variable 'x'.

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


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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2

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 = {-2, -1.75}

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