4x(6x-10)=5x(4x+8)

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Solution for 4x(6x-10)=5x(4x+8) equation: 


Simplifying
4x(6x + -10) = 5x(4x + 8)

Reorder the terms:
4x(-10 + 6x) = 5x(4x + 8)
(-10 * 4x + 6x * 4x) = 5x(4x + 8)
(-40x + 24x2) = 5x(4x + 8)

Reorder the terms:
-40x + 24x2 = 5x(8 + 4x)
-40x + 24x2 = (8 * 5x + 4x * 5x)
-40x + 24x2 = (40x + 20x2)

Solving
-40x + 24x2 = 40x + 20x2

Solving for variable 'x'.

Reorder the terms:
-40x + -40x + 24x2 + -20x2 = 40x + 20x2 + -40x + -20x2

Combine like terms: -40x + -40x = -80x
-80x + 24x2 + -20x2 = 40x + 20x2 + -40x + -20x2

Combine like terms: 24x2 + -20x2 = 4x2
-80x + 4x2 = 40x + 20x2 + -40x + -20x2

Reorder the terms:
-80x + 4x2 = 40x + -40x + 20x2 + -20x2

Combine like terms: 40x + -40x = 0
-80x + 4x2 = 0 + 20x2 + -20x2
-80x + 4x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-80x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-20 + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
-20 + x = 0

Solving
-20 + x = 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 + x = 0 + 20

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

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

Simplifying
x = 20
Solution
x = {0, 20}

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