(4x+7)(7x+22)=0

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Solution for (4x+7)(7x+22)=0 equation: 


Simplifying
(4x + 7)(7x + 22) = 0

Reorder the terms:
(7 + 4x)(7x + 22) = 0

Reorder the terms:
(7 + 4x)(22 + 7x) = 0

Multiply (7 + 4x) * (22 + 7x)
(7(22 + 7x) + 4x * (22 + 7x)) = 0
((22 * 7 + 7x * 7) + 4x * (22 + 7x)) = 0
((154 + 49x) + 4x * (22 + 7x)) = 0
(154 + 49x + (22 * 4x + 7x * 4x)) = 0
(154 + 49x + (88x + 28x2)) = 0

Combine like terms: 49x + 88x = 137x
(154 + 137x + 28x2) = 0

Solving
154 + 137x + 28x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(22 + 7x)(7 + 4x) = 0


Subproblem 1
Set the factor '(22 + 7x)' equal to zero and attempt to solve:

Simplifying
22 + 7x = 0

Solving
22 + 7x = 0

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

Add '-22' to each side of the equation.
22 + -22 + 7x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 7x = 0 + -22
7x = 0 + -22

Combine like terms: 0 + -22 = -22
7x = -22

Divide each side by '7'.
x = -3.142857143

Simplifying
x = -3.142857143

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 = {-3.142857143, -1.75}

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