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

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


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

Reorder the terms:
4x(8 + 6x) = 5x(6x + -10)
(8 * 4x + 6x * 4x) = 5x(6x + -10)
(32x + 24x2) = 5x(6x + -10)

Reorder the terms:
32x + 24x2 = 5x(-10 + 6x)
32x + 24x2 = (-10 * 5x + 6x * 5x)
32x + 24x2 = (-50x + 30x2)

Solving
32x + 24x2 = -50x + 30x2

Solving for variable 'x'.

Reorder the terms:
32x + 50x + 24x2 + -30x2 = -50x + 30x2 + 50x + -30x2

Combine like terms: 32x + 50x = 82x
82x + 24x2 + -30x2 = -50x + 30x2 + 50x + -30x2

Combine like terms: 24x2 + -30x2 = -6x2
82x + -6x2 = -50x + 30x2 + 50x + -30x2

Reorder the terms:
82x + -6x2 = -50x + 50x + 30x2 + -30x2

Combine like terms: -50x + 50x = 0
82x + -6x2 = 0 + 30x2 + -30x2
82x + -6x2 = 30x2 + -30x2

Combine like terms: 30x2 + -30x2 = 0
82x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(41 + -3x) = 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 '(41 + -3x)' equal to zero and attempt to solve:

Simplifying
41 + -3x = 0

Solving
41 + -3x = 0

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

Add '-41' to each side of the equation.
41 + -41 + -3x = 0 + -41

Combine like terms: 41 + -41 = 0
0 + -3x = 0 + -41
-3x = 0 + -41

Combine like terms: 0 + -41 = -41
-3x = -41

Divide each side by '-3'.
x = 13.66666667

Simplifying
x = 13.66666667
Solution
x = {0, 13.66666667}

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