4x(x+6)=6x

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Solution for 4x(x+6)=6x equation: 


Simplifying
4x(x + 6) = 6x

Reorder the terms:
4x(6 + x) = 6x
(6 * 4x + x * 4x) = 6x
(24x + 4x2) = 6x

Solving
24x + 4x2 = 6x

Solving for variable 'x'.

Reorder the terms:
24x + -6x + 4x2 = 6x + -6x

Combine like terms: 24x + -6x = 18x
18x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
18x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(9 + 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 '(9 + 2x)' equal to zero and attempt to solve:

Simplifying
9 + 2x = 0

Solving
9 + 2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2x = 0 + -9
2x = 0 + -9

Combine like terms: 0 + -9 = -9
2x = -9

Divide each side by '2'.
x = -4.5

Simplifying
x = -4.5
Solution
x = {0, -4.5}

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