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

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


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

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

Reorder the terms:
-40x + 24x2 = 5x(10 + 4x)
-40x + 24x2 = (10 * 5x + 4x * 5x)
-40x + 24x2 = (50x + 20x2)

Solving
-40x + 24x2 = 50x + 20x2

Solving for variable 'x'.

Reorder the terms:
-40x + -50x + 24x2 + -20x2 = 50x + 20x2 + -50x + -20x2

Combine like terms: -40x + -50x = -90x
-90x + 24x2 + -20x2 = 50x + 20x2 + -50x + -20x2

Combine like terms: 24x2 + -20x2 = 4x2
-90x + 4x2 = 50x + 20x2 + -50x + -20x2

Reorder the terms:
-90x + 4x2 = 50x + -50x + 20x2 + -20x2

Combine like terms: 50x + -50x = 0
-90x + 4x2 = 0 + 20x2 + -20x2
-90x + 4x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-90x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-45 + 2x) = 0

Ignore the factor 2.

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 '(-45 + 2x)' equal to zero and attempt to solve:

Simplifying
-45 + 2x = 0

Solving
-45 + 2x = 0

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

Add '45' to each side of the equation.
-45 + 45 + 2x = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 2x = 0 + 45
2x = 0 + 45

Combine like terms: 0 + 45 = 45
2x = 45

Divide each side by '2'.
x = 22.5

Simplifying
x = 22.5
Solution
x = {0, 22.5}

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