(8x-3)(-10x+3)=(8x-3)(3)

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Solution for (8x-3)(-10x+3)=(8x-3)(3) equation: 


Simplifying
(8x + -3)(-10x + 3) = (8x + -3)(3)

Reorder the terms:
(-3 + 8x)(-10x + 3) = (8x + -3)(3)

Reorder the terms:
(-3 + 8x)(3 + -10x) = (8x + -3)(3)

Multiply (-3 + 8x) * (3 + -10x)
(-3(3 + -10x) + 8x * (3 + -10x)) = (8x + -3)(3)
((3 * -3 + -10x * -3) + 8x * (3 + -10x)) = (8x + -3)(3)
((-9 + 30x) + 8x * (3 + -10x)) = (8x + -3)(3)
(-9 + 30x + (3 * 8x + -10x * 8x)) = (8x + -3)(3)
(-9 + 30x + (24x + -80x2)) = (8x + -3)(3)

Combine like terms: 30x + 24x = 54x
(-9 + 54x + -80x2) = (8x + -3)(3)

Reorder the terms:
-9 + 54x + -80x2 = (-3 + 8x)(3)

Reorder the terms for easier multiplication:
-9 + 54x + -80x2 = 3(-3 + 8x)
-9 + 54x + -80x2 = (-3 * 3 + 8x * 3)
-9 + 54x + -80x2 = (-9 + 24x)

Add '9' to each side of the equation.
-9 + 54x + 9 + -80x2 = -9 + 9 + 24x

Reorder the terms:
-9 + 9 + 54x + -80x2 = -9 + 9 + 24x

Combine like terms: -9 + 9 = 0
0 + 54x + -80x2 = -9 + 9 + 24x
54x + -80x2 = -9 + 9 + 24x

Combine like terms: -9 + 9 = 0
54x + -80x2 = 0 + 24x
54x + -80x2 = 24x

Solving
54x + -80x2 = 24x

Solving for variable 'x'.

Reorder the terms:
54x + -24x + -80x2 = 24x + -24x

Combine like terms: 54x + -24x = 30x
30x + -80x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
30x + -80x2 = 0

Factor out the Greatest Common Factor (GCF), '10x'.
10x(3 + -8x) = 0

Ignore the factor 10.

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 '(3 + -8x)' equal to zero and attempt to solve:

Simplifying
3 + -8x = 0

Solving
3 + -8x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -8x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8x = 0 + -3
-8x = 0 + -3

Combine like terms: 0 + -3 = -3
-8x = -3

Divide each side by '-8'.
x = 0.375

Simplifying
x = 0.375
Solution
x = {0, 0.375}

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