6(4x-5)=(2x-3)(4x-5)

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Solution for 6(4x-5)=(2x-3)(4x-5) equation: 


Simplifying
6(4x + -5) = (2x + -3)(4x + -5)

Reorder the terms:
6(-5 + 4x) = (2x + -3)(4x + -5)
(-5 * 6 + 4x * 6) = (2x + -3)(4x + -5)
(-30 + 24x) = (2x + -3)(4x + -5)

Reorder the terms:
-30 + 24x = (-3 + 2x)(4x + -5)

Reorder the terms:
-30 + 24x = (-3 + 2x)(-5 + 4x)

Multiply (-3 + 2x) * (-5 + 4x)
-30 + 24x = (-3(-5 + 4x) + 2x * (-5 + 4x))
-30 + 24x = ((-5 * -3 + 4x * -3) + 2x * (-5 + 4x))
-30 + 24x = ((15 + -12x) + 2x * (-5 + 4x))
-30 + 24x = (15 + -12x + (-5 * 2x + 4x * 2x))
-30 + 24x = (15 + -12x + (-10x + 8x2))

Combine like terms: -12x + -10x = -22x
-30 + 24x = (15 + -22x + 8x2)

Solving
-30 + 24x = 15 + -22x + 8x2

Solving for variable 'x'.

Reorder the terms:
-30 + -15 + 24x + 22x + -8x2 = 15 + -22x + 8x2 + -15 + 22x + -8x2

Combine like terms: -30 + -15 = -45
-45 + 24x + 22x + -8x2 = 15 + -22x + 8x2 + -15 + 22x + -8x2

Combine like terms: 24x + 22x = 46x
-45 + 46x + -8x2 = 15 + -22x + 8x2 + -15 + 22x + -8x2

Reorder the terms:
-45 + 46x + -8x2 = 15 + -15 + -22x + 22x + 8x2 + -8x2

Combine like terms: 15 + -15 = 0
-45 + 46x + -8x2 = 0 + -22x + 22x + 8x2 + -8x2
-45 + 46x + -8x2 = -22x + 22x + 8x2 + -8x2

Combine like terms: -22x + 22x = 0
-45 + 46x + -8x2 = 0 + 8x2 + -8x2
-45 + 46x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-45 + 46x + -8x2 = 0

Factor a trinomial.
(-9 + 2x)(5 + -4x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {4.5, 1.25}

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