x(x-1)=4(3x-10)

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Solution for x(x-1)=4(3x-10) equation:


Simplifying
x(x + -1) = 4(3x + -10)

Reorder the terms:
x(-1 + x) = 4(3x + -10)
(-1 * x + x * x) = 4(3x + -10)
(-1x + x2) = 4(3x + -10)

Reorder the terms:
-1x + x2 = 4(-10 + 3x)
-1x + x2 = (-10 * 4 + 3x * 4)
-1x + x2 = (-40 + 12x)

Solving
-1x + x2 = -40 + 12x

Solving for variable 'x'.

Reorder the terms:
40 + -1x + -12x + x2 = -40 + 12x + 40 + -12x

Combine like terms: -1x + -12x = -13x
40 + -13x + x2 = -40 + 12x + 40 + -12x

Reorder the terms:
40 + -13x + x2 = -40 + 40 + 12x + -12x

Combine like terms: -40 + 40 = 0
40 + -13x + x2 = 0 + 12x + -12x
40 + -13x + x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
40 + -13x + x2 = 0

Factor a trinomial.
(5 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {5, 8}

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