3x(x-1)-x(x-8)=3

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Solution for 3x(x-1)-x(x-8)=3 equation:


Simplifying
3x(x + -1) + -1x(x + -8) = 3

Reorder the terms:
3x(-1 + x) + -1x(x + -8) = 3
(-1 * 3x + x * 3x) + -1x(x + -8) = 3
(-3x + 3x2) + -1x(x + -8) = 3

Reorder the terms:
-3x + 3x2 + -1x(-8 + x) = 3
-3x + 3x2 + (-8 * -1x + x * -1x) = 3
-3x + 3x2 + (8x + -1x2) = 3

Reorder the terms:
-3x + 8x + 3x2 + -1x2 = 3

Combine like terms: -3x + 8x = 5x
5x + 3x2 + -1x2 = 3

Combine like terms: 3x2 + -1x2 = 2x2
5x + 2x2 = 3

Solving
5x + 2x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 5x + 2x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 5x + 2x2 = 0

Factor a trinomial.
(-3 + -1x)(1 + -2x) = 0

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

Subproblem 2

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

Solution

x = {-3, 0.5}

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