5(x-6)-6x(x-5)=x+5-(x-4)

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Solution for 5(x-6)-6x(x-5)=x+5-(x-4) equation: 


Simplifying
5(x + -6) + -6x(x + -5) = x + 5 + -1(x + -4)

Reorder the terms:
5(-6 + x) + -6x(x + -5) = x + 5 + -1(x + -4)
(-6 * 5 + x * 5) + -6x(x + -5) = x + 5 + -1(x + -4)
(-30 + 5x) + -6x(x + -5) = x + 5 + -1(x + -4)

Reorder the terms:
-30 + 5x + -6x(-5 + x) = x + 5 + -1(x + -4)
-30 + 5x + (-5 * -6x + x * -6x) = x + 5 + -1(x + -4)
-30 + 5x + (30x + -6x2) = x + 5 + -1(x + -4)

Combine like terms: 5x + 30x = 35x
-30 + 35x + -6x2 = x + 5 + -1(x + -4)

Reorder the terms:
-30 + 35x + -6x2 = x + 5 + -1(-4 + x)
-30 + 35x + -6x2 = x + 5 + (-4 * -1 + x * -1)
-30 + 35x + -6x2 = x + 5 + (4 + -1x)

Reorder the terms:
-30 + 35x + -6x2 = 5 + 4 + x + -1x

Combine like terms: 5 + 4 = 9
-30 + 35x + -6x2 = 9 + x + -1x

Combine like terms: x + -1x = 0
-30 + 35x + -6x2 = 9 + 0
-30 + 35x + -6x2 = 9

Solving
-30 + 35x + -6x2 = 9

Solving for variable 'x'.

Reorder the terms:
-30 + -9 + 35x + -6x2 = 9 + -9

Combine like terms: -30 + -9 = -39
-39 + 35x + -6x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-39 + 35x + -6x2 = 0

Factor a trinomial.
(-13 + 3x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-13 + 3x)' equal to zero and attempt to solve:

Simplifying
-13 + 3x = 0

Solving
-13 + 3x = 0

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

Add '13' to each side of the equation.
-13 + 13 + 3x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 3x = 0 + 13
3x = 0 + 13

Combine like terms: 0 + 13 = 13
3x = 13

Divide each side by '3'.
x = 4.333333333

Simplifying
x = 4.333333333

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {4.333333333, 1.5}

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