4x(x+1)=6x(2x-5)

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Solution for 4x(x+1)=6x(2x-5) equation: 


Simplifying
4x(x + 1) = 6x(2x + -5)

Reorder the terms:
4x(1 + x) = 6x(2x + -5)
(1 * 4x + x * 4x) = 6x(2x + -5)
(4x + 4x2) = 6x(2x + -5)

Reorder the terms:
4x + 4x2 = 6x(-5 + 2x)
4x + 4x2 = (-5 * 6x + 2x * 6x)
4x + 4x2 = (-30x + 12x2)

Solving
4x + 4x2 = -30x + 12x2

Solving for variable 'x'.

Reorder the terms:
4x + 30x + 4x2 + -12x2 = -30x + 12x2 + 30x + -12x2

Combine like terms: 4x + 30x = 34x
34x + 4x2 + -12x2 = -30x + 12x2 + 30x + -12x2

Combine like terms: 4x2 + -12x2 = -8x2
34x + -8x2 = -30x + 12x2 + 30x + -12x2

Reorder the terms:
34x + -8x2 = -30x + 30x + 12x2 + -12x2

Combine like terms: -30x + 30x = 0
34x + -8x2 = 0 + 12x2 + -12x2
34x + -8x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
34x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(17 + -4x) = 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 '(17 + -4x)' equal to zero and attempt to solve:

Simplifying
17 + -4x = 0

Solving
17 + -4x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -4x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -4x = 0 + -17
-4x = 0 + -17

Combine like terms: 0 + -17 = -17
-4x = -17

Divide each side by '-4'.
x = 4.25

Simplifying
x = 4.25
Solution
x = {0, 4.25}

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