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

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


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

Reorder the terms:
4x(-6 + x) = (2x + 1)(x + -6)
(-6 * 4x + x * 4x) = (2x + 1)(x + -6)
(-24x + 4x2) = (2x + 1)(x + -6)

Reorder the terms:
-24x + 4x2 = (1 + 2x)(x + -6)

Reorder the terms:
-24x + 4x2 = (1 + 2x)(-6 + x)

Multiply (1 + 2x) * (-6 + x)
-24x + 4x2 = (1(-6 + x) + 2x * (-6 + x))
-24x + 4x2 = ((-6 * 1 + x * 1) + 2x * (-6 + x))
-24x + 4x2 = ((-6 + 1x) + 2x * (-6 + x))
-24x + 4x2 = (-6 + 1x + (-6 * 2x + x * 2x))
-24x + 4x2 = (-6 + 1x + (-12x + 2x2))

Combine like terms: 1x + -12x = -11x
-24x + 4x2 = (-6 + -11x + 2x2)

Solving
-24x + 4x2 = -6 + -11x + 2x2

Solving for variable 'x'.

Reorder the terms:
6 + -24x + 11x + 4x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2

Combine like terms: -24x + 11x = -13x
6 + -13x + 4x2 + -2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
6 + -13x + 2x2 = -6 + -11x + 2x2 + 6 + 11x + -2x2

Reorder the terms:
6 + -13x + 2x2 = -6 + 6 + -11x + 11x + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
6 + -13x + 2x2 = 0 + -11x + 11x + 2x2 + -2x2
6 + -13x + 2x2 = -11x + 11x + 2x2 + -2x2

Combine like terms: -11x + 11x = 0
6 + -13x + 2x2 = 0 + 2x2 + -2x2
6 + -13x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + -13x + 2x2 = 0

Factor a trinomial.
(1 + -2x)(6 + -1x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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 = {0.5, 6}

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