5x(x-8)=12x^2-41x

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Solution for 5x(x-8)=12x^2-41x equation: 


Simplifying
5x(x + -8) = 12x2 + -41x

Reorder the terms:
5x(-8 + x) = 12x2 + -41x
(-8 * 5x + x * 5x) = 12x2 + -41x
(-40x + 5x2) = 12x2 + -41x

Reorder the terms:
-40x + 5x2 = -41x + 12x2

Solving
-40x + 5x2 = -41x + 12x2

Solving for variable 'x'.

Reorder the terms:
-40x + 41x + 5x2 + -12x2 = -41x + 12x2 + 41x + -12x2

Combine like terms: -40x + 41x = 1x
1x + 5x2 + -12x2 = -41x + 12x2 + 41x + -12x2

Combine like terms: 5x2 + -12x2 = -7x2
1x + -7x2 = -41x + 12x2 + 41x + -12x2

Reorder the terms:
1x + -7x2 = -41x + 41x + 12x2 + -12x2

Combine like terms: -41x + 41x = 0
1x + -7x2 = 0 + 12x2 + -12x2
1x + -7x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
1x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -7x) = 0


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 '(1 + -7x)' equal to zero and attempt to solve:

Simplifying
1 + -7x = 0

Solving
1 + -7x = 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 + -7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7x = 0 + -1
-7x = 0 + -1

Combine like terms: 0 + -1 = -1
-7x = -1

Divide each side by '-7'.
x = 0.1428571429

Simplifying
x = 0.1428571429
Solution
x = {0, 0.1428571429}

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