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

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


Simplifying
2x(2x + -3) + -1(3x + -1)(x + 1) = -6

Reorder the terms:
2x(-3 + 2x) + -1(3x + -1)(x + 1) = -6
(-3 * 2x + 2x * 2x) + -1(3x + -1)(x + 1) = -6
(-6x + 4x2) + -1(3x + -1)(x + 1) = -6

Reorder the terms:
-6x + 4x2 + -1(-1 + 3x)(x + 1) = -6

Reorder the terms:
-6x + 4x2 + -1(-1 + 3x)(1 + x) = -6

Multiply (-1 + 3x) * (1 + x)
-6x + 4x2 + -1(-1(1 + x) + 3x * (1 + x)) = -6
-6x + 4x2 + -1((1 * -1 + x * -1) + 3x * (1 + x)) = -6
-6x + 4x2 + -1((-1 + -1x) + 3x * (1 + x)) = -6
-6x + 4x2 + -1(-1 + -1x + (1 * 3x + x * 3x)) = -6
-6x + 4x2 + -1(-1 + -1x + (3x + 3x2)) = -6

Combine like terms: -1x + 3x = 2x
-6x + 4x2 + -1(-1 + 2x + 3x2) = -6
-6x + 4x2 + (-1 * -1 + 2x * -1 + 3x2 * -1) = -6
-6x + 4x2 + (1 + -2x + -3x2) = -6

Reorder the terms:
1 + -6x + -2x + 4x2 + -3x2 = -6

Combine like terms: -6x + -2x = -8x
1 + -8x + 4x2 + -3x2 = -6

Combine like terms: 4x2 + -3x2 = 1x2
1 + -8x + 1x2 = -6

Solving
1 + -8x + 1x2 = -6

Solving for variable 'x'.

Reorder the terms:
1 + 6 + -8x + 1x2 = -6 + 6

Combine like terms: 1 + 6 = 7
7 + -8x + 1x2 = -6 + 6

Combine like terms: -6 + 6 = 0
7 + -8x + 1x2 = 0

Factor a trinomial.
(1 + -1x)(7 + -1x) = 0


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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {1, 7}

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