4x(3x-1)-(x-1)(x-1)=20-3x(8-x)

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Solution for 4x(3x-1)-(x-1)(x-1)=20-3x(8-x) equation:


Simplifying
4x(3x + -1) + -1(x + -1)(x + -1) = 20 + -3x(8 + -1x)

Reorder the terms:
4x(-1 + 3x) + -1(x + -1)(x + -1) = 20 + -3x(8 + -1x)
(-1 * 4x + 3x * 4x) + -1(x + -1)(x + -1) = 20 + -3x(8 + -1x)
(-4x + 12x2) + -1(x + -1)(x + -1) = 20 + -3x(8 + -1x)

Reorder the terms:
-4x + 12x2 + -1(-1 + x)(x + -1) = 20 + -3x(8 + -1x)

Reorder the terms:
-4x + 12x2 + -1(-1 + x)(-1 + x) = 20 + -3x(8 + -1x)

Multiply (-1 + x) * (-1 + x)
-4x + 12x2 + -1(-1(-1 + x) + x(-1 + x)) = 20 + -3x(8 + -1x)
-4x + 12x2 + -1((-1 * -1 + x * -1) + x(-1 + x)) = 20 + -3x(8 + -1x)
-4x + 12x2 + -1((1 + -1x) + x(-1 + x)) = 20 + -3x(8 + -1x)
-4x + 12x2 + -1(1 + -1x + (-1 * x + x * x)) = 20 + -3x(8 + -1x)
-4x + 12x2 + -1(1 + -1x + (-1x + x2)) = 20 + -3x(8 + -1x)

Combine like terms: -1x + -1x = -2x
-4x + 12x2 + -1(1 + -2x + x2) = 20 + -3x(8 + -1x)
-4x + 12x2 + (1 * -1 + -2x * -1 + x2 * -1) = 20 + -3x(8 + -1x)
-4x + 12x2 + (-1 + 2x + -1x2) = 20 + -3x(8 + -1x)

Reorder the terms:
-1 + -4x + 2x + 12x2 + -1x2 = 20 + -3x(8 + -1x)

Combine like terms: -4x + 2x = -2x
-1 + -2x + 12x2 + -1x2 = 20 + -3x(8 + -1x)

Combine like terms: 12x2 + -1x2 = 11x2
-1 + -2x + 11x2 = 20 + -3x(8 + -1x)
-1 + -2x + 11x2 = 20 + (8 * -3x + -1x * -3x)
-1 + -2x + 11x2 = 20 + (-24x + 3x2)

Solving
-1 + -2x + 11x2 = 20 + -24x + 3x2

Solving for variable 'x'.

Reorder the terms:
-1 + -20 + -2x + 24x + 11x2 + -3x2 = 20 + -24x + 3x2 + -20 + 24x + -3x2

Combine like terms: -1 + -20 = -21
-21 + -2x + 24x + 11x2 + -3x2 = 20 + -24x + 3x2 + -20 + 24x + -3x2

Combine like terms: -2x + 24x = 22x
-21 + 22x + 11x2 + -3x2 = 20 + -24x + 3x2 + -20 + 24x + -3x2

Combine like terms: 11x2 + -3x2 = 8x2
-21 + 22x + 8x2 = 20 + -24x + 3x2 + -20 + 24x + -3x2

Reorder the terms:
-21 + 22x + 8x2 = 20 + -20 + -24x + 24x + 3x2 + -3x2

Combine like terms: 20 + -20 = 0
-21 + 22x + 8x2 = 0 + -24x + 24x + 3x2 + -3x2
-21 + 22x + 8x2 = -24x + 24x + 3x2 + -3x2

Combine like terms: -24x + 24x = 0
-21 + 22x + 8x2 = 0 + 3x2 + -3x2
-21 + 22x + 8x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-21 + 22x + 8x2 = 0

Factor a trinomial.
(-7 + -2x)(3 + -4x) = 0


Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-3.5, 0.75}

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