4x(x-6)=(3x+4)(x-6)

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Solution for 4x(x-6)=(3x+4)(x-6) equation: 


Simplifying
4x(x + -6) = (3x + 4)(x + -6)

Reorder the terms:
4x(-6 + x) = (3x + 4)(x + -6)
(-6 * 4x + x * 4x) = (3x + 4)(x + -6)
(-24x + 4x2) = (3x + 4)(x + -6)

Reorder the terms:
-24x + 4x2 = (4 + 3x)(x + -6)

Reorder the terms:
-24x + 4x2 = (4 + 3x)(-6 + x)

Multiply (4 + 3x) * (-6 + x)
-24x + 4x2 = (4(-6 + x) + 3x * (-6 + x))
-24x + 4x2 = ((-6 * 4 + x * 4) + 3x * (-6 + x))
-24x + 4x2 = ((-24 + 4x) + 3x * (-6 + x))
-24x + 4x2 = (-24 + 4x + (-6 * 3x + x * 3x))
-24x + 4x2 = (-24 + 4x + (-18x + 3x2))

Combine like terms: 4x + -18x = -14x
-24x + 4x2 = (-24 + -14x + 3x2)

Solving
-24x + 4x2 = -24 + -14x + 3x2

Solving for variable 'x'.

Reorder the terms:
24 + -24x + 14x + 4x2 + -3x2 = -24 + -14x + 3x2 + 24 + 14x + -3x2

Combine like terms: -24x + 14x = -10x
24 + -10x + 4x2 + -3x2 = -24 + -14x + 3x2 + 24 + 14x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
24 + -10x + 1x2 = -24 + -14x + 3x2 + 24 + 14x + -3x2

Reorder the terms:
24 + -10x + 1x2 = -24 + 24 + -14x + 14x + 3x2 + -3x2

Combine like terms: -24 + 24 = 0
24 + -10x + 1x2 = 0 + -14x + 14x + 3x2 + -3x2
24 + -10x + 1x2 = -14x + 14x + 3x2 + -3x2

Combine like terms: -14x + 14x = 0
24 + -10x + 1x2 = 0 + 3x2 + -3x2
24 + -10x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
24 + -10x + 1x2 = 0

Factor a trinomial.
(4 + -1x)(6 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {4, 6}

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