3(x^2-x-6)+(x-3)(x-1)=0

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Solution for 3(x^2-x-6)+(x-3)(x-1)=0 equation: 


Simplifying
3(x2 + -1x + -6) + (x + -3)(x + -1) = 0

Reorder the terms:
3(-6 + -1x + x2) + (x + -3)(x + -1) = 0
(-6 * 3 + -1x * 3 + x2 * 3) + (x + -3)(x + -1) = 0
(-18 + -3x + 3x2) + (x + -3)(x + -1) = 0

Reorder the terms:
-18 + -3x + 3x2 + (-3 + x)(x + -1) = 0

Reorder the terms:
-18 + -3x + 3x2 + (-3 + x)(-1 + x) = 0

Multiply (-3 + x) * (-1 + x)
-18 + -3x + 3x2 + (-3(-1 + x) + x(-1 + x)) = 0
-18 + -3x + 3x2 + ((-1 * -3 + x * -3) + x(-1 + x)) = 0
-18 + -3x + 3x2 + ((3 + -3x) + x(-1 + x)) = 0
-18 + -3x + 3x2 + (3 + -3x + (-1 * x + x * x)) = 0
-18 + -3x + 3x2 + (3 + -3x + (-1x + x2)) = 0

Combine like terms: -3x + -1x = -4x
-18 + -3x + 3x2 + (3 + -4x + x2) = 0

Reorder the terms:
-18 + 3 + -3x + -4x + 3x2 + x2 = 0

Combine like terms: -18 + 3 = -15
-15 + -3x + -4x + 3x2 + x2 = 0

Combine like terms: -3x + -4x = -7x
-15 + -7x + 3x2 + x2 = 0

Combine like terms: 3x2 + x2 = 4x2
-15 + -7x + 4x2 = 0

Solving
-15 + -7x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -4x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 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 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 2
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
Solution
x = {-1.25, 3}

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