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

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


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

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

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

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

Multiply (1 + 2x) * (-4 + x)
-24x + 6x2 = (1(-4 + x) + 2x * (-4 + x))
-24x + 6x2 = ((-4 * 1 + x * 1) + 2x * (-4 + x))
-24x + 6x2 = ((-4 + 1x) + 2x * (-4 + x))
-24x + 6x2 = (-4 + 1x + (-4 * 2x + x * 2x))
-24x + 6x2 = (-4 + 1x + (-8x + 2x2))

Combine like terms: 1x + -8x = -7x
-24x + 6x2 = (-4 + -7x + 2x2)

Solving
-24x + 6x2 = -4 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
4 + -24x + 7x + 6x2 + -2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2

Combine like terms: -24x + 7x = -17x
4 + -17x + 6x2 + -2x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
4 + -17x + 4x2 = -4 + -7x + 2x2 + 4 + 7x + -2x2

Reorder the terms:
4 + -17x + 4x2 = -4 + 4 + -7x + 7x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
4 + -17x + 4x2 = 0 + -7x + 7x + 2x2 + -2x2
4 + -17x + 4x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
4 + -17x + 4x2 = 0 + 2x2 + -2x2
4 + -17x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
4 + -17x + 4x2 = 0

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


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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

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

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

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
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
Solution
x = {0.25, 4}

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