4x(8x-10)=5x(4x+8)

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Solution for 4x(8x-10)=5x(4x+8) equation: 


Simplifying
4x(8x + -10) = 5x(4x + 8)

Reorder the terms:
4x(-10 + 8x) = 5x(4x + 8)
(-10 * 4x + 8x * 4x) = 5x(4x + 8)
(-40x + 32x2) = 5x(4x + 8)

Reorder the terms:
-40x + 32x2 = 5x(8 + 4x)
-40x + 32x2 = (8 * 5x + 4x * 5x)
-40x + 32x2 = (40x + 20x2)

Solving
-40x + 32x2 = 40x + 20x2

Solving for variable 'x'.

Reorder the terms:
-40x + -40x + 32x2 + -20x2 = 40x + 20x2 + -40x + -20x2

Combine like terms: -40x + -40x = -80x
-80x + 32x2 + -20x2 = 40x + 20x2 + -40x + -20x2

Combine like terms: 32x2 + -20x2 = 12x2
-80x + 12x2 = 40x + 20x2 + -40x + -20x2

Reorder the terms:
-80x + 12x2 = 40x + -40x + 20x2 + -20x2

Combine like terms: 40x + -40x = 0
-80x + 12x2 = 0 + 20x2 + -20x2
-80x + 12x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-80x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-20 + 3x) = 0

Ignore the factor 4.

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 '(-20 + 3x)' equal to zero and attempt to solve:

Simplifying
-20 + 3x = 0

Solving
-20 + 3x = 0

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

Add '20' to each side of the equation.
-20 + 20 + 3x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 3x = 0 + 20
3x = 0 + 20

Combine like terms: 0 + 20 = 20
3x = 20

Divide each side by '3'.
x = 6.666666667

Simplifying
x = 6.666666667
Solution
x = {0, 6.666666667}

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