(4x+5)x(4x+5)=0

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Solution for (4x+5)x(4x+5)=0 equation: 


Simplifying
(4x + 5) * x(4x + 5) = 0

Reorder the terms:
(5 + 4x) * x(4x + 5) = 0

Reorder the terms:
(5 + 4x) * x(5 + 4x) = 0

Reorder the terms for easier multiplication:
x(5 + 4x)(5 + 4x) = 0

Multiply (5 + 4x) * (5 + 4x)
x(5(5 + 4x) + 4x * (5 + 4x)) = 0
x((5 * 5 + 4x * 5) + 4x * (5 + 4x)) = 0
x((25 + 20x) + 4x * (5 + 4x)) = 0
x(25 + 20x + (5 * 4x + 4x * 4x)) = 0
x(25 + 20x + (20x + 16x2)) = 0

Combine like terms: 20x + 20x = 40x
x(25 + 40x + 16x2) = 0
(25 * x + 40x * x + 16x2 * x) = 0
(25x + 40x2 + 16x3) = 0

Solving
25x + 40x2 + 16x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(25 + 40x + 16x2) = 0

Factor a trinomial.
x((5 + 4x)(5 + 4x)) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 3
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25
Solution
x = {0, -1.25, -1.25}

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