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

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


Simplifying
x2(2x + 7)(x + 7) = 0

Reorder the terms:
x2(7 + 2x)(x + 7) = 0

Reorder the terms:
x2(7 + 2x)(7 + x) = 0

Multiply (7 + 2x) * (7 + x)
x2(7(7 + x) + 2x * (7 + x)) = 0
x2((7 * 7 + x * 7) + 2x * (7 + x)) = 0
x2((49 + 7x) + 2x * (7 + x)) = 0
x2(49 + 7x + (7 * 2x + x * 2x)) = 0
x2(49 + 7x + (14x + 2x2)) = 0

Combine like terms: 7x + 14x = 21x
x2(49 + 21x + 2x2) = 0
(49 * x2 + 21x * x2 + 2x2 * x2) = 0
(49x2 + 21x3 + 2x4) = 0

Solving
49x2 + 21x3 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(49 + 21x + 2x2) = 0

Factor a trinomial.
x2((7 + x)(7 + 2x)) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
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 3
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 = {0, -7, -3.5}

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