64(4-4x+x^2)=4x^2

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Solution for 64(4-4x+x^2)=4x^2 equation: 


Simplifying
64(4 + -4x + x2) = 4x2
(4 * 64 + -4x * 64 + x2 * 64) = 4x2
(256 + -256x + 64x2) = 4x2

Solving
256 + -256x + 64x2 = 4x2

Solving for variable 'x'.

Combine like terms: 64x2 + -4x2 = 60x2
256 + -256x + 60x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
256 + -256x + 60x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(64 + -64x + 15x2) = 0

Factor a trinomial.
4((8 + -5x)(8 + -3x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Divide each side by '-5'.
x = 1.6

Simplifying
x = 1.6

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {1.6, 2.666666667}

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