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

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


Simplifying
x2(4x + 7)(4x + -7) = 0

Reorder the terms:
x2(7 + 4x)(4x + -7) = 0

Reorder the terms:
x2(7 + 4x)(-7 + 4x) = 0

Multiply (7 + 4x) * (-7 + 4x)
x2(7(-7 + 4x) + 4x * (-7 + 4x)) = 0
x2((-7 * 7 + 4x * 7) + 4x * (-7 + 4x)) = 0
x2((-49 + 28x) + 4x * (-7 + 4x)) = 0
x2(-49 + 28x + (-7 * 4x + 4x * 4x)) = 0
x2(-49 + 28x + (-28x + 16x2)) = 0

Combine like terms: 28x + -28x = 0
x2(-49 + 0 + 16x2) = 0
x2(-49 + 16x2) = 0
(-49 * x2 + 16x2 * x2) = 0
(-49x2 + 16x4) = 0

Solving
-49x2 + 16x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-49 + 16x2) = 0

Factor a difference between two squares.
x2((7 + 4x)(-7 + 4x)) = 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 + 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

Subproblem 3
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 = {0, -1.75, 1.75}

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