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

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


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

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

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

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

Combine like terms: 28x + 7x = 35x
(49 + 35x + 4x2) = 0

Solving
49 + 35x + 4x2 = 0

Solving for variable 'x'.

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


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

Simplifying
7 + x = 0

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

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

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

Simplifying
x = -7

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 = {-7, -1.75}

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