4x(x+5)=6x(12+x)

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Solution for 4x(x+5)=6x(12+x) equation: 


Simplifying
4x(x + 5) = 6x(12 + x)

Reorder the terms:
4x(5 + x) = 6x(12 + x)
(5 * 4x + x * 4x) = 6x(12 + x)
(20x + 4x2) = 6x(12 + x)
20x + 4x2 = (12 * 6x + x * 6x)
20x + 4x2 = (72x + 6x2)

Solving
20x + 4x2 = 72x + 6x2

Solving for variable 'x'.

Reorder the terms:
20x + -72x + 4x2 + -6x2 = 72x + 6x2 + -72x + -6x2

Combine like terms: 20x + -72x = -52x
-52x + 4x2 + -6x2 = 72x + 6x2 + -72x + -6x2

Combine like terms: 4x2 + -6x2 = -2x2
-52x + -2x2 = 72x + 6x2 + -72x + -6x2

Reorder the terms:
-52x + -2x2 = 72x + -72x + 6x2 + -6x2

Combine like terms: 72x + -72x = 0
-52x + -2x2 = 0 + 6x2 + -6x2
-52x + -2x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-52x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(26 + x) = 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 '(26 + x)' equal to zero and attempt to solve:

Simplifying
26 + x = 0

Solving
26 + x = 0

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

Add '-26' to each side of the equation.
26 + -26 + x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + x = 0 + -26
x = 0 + -26

Combine like terms: 0 + -26 = -26
x = -26

Simplifying
x = -26
Solution
x = {0, -26}

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