2x^2=(x+2)(x-3)+12

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Solution for 2x^2=(x+2)(x-3)+12 equation:


Simplifying
2x2 = (x + 2)(x + -3) + 12

Reorder the terms:
2x2 = (2 + x)(x + -3) + 12

Reorder the terms:
2x2 = (2 + x)(-3 + x) + 12

Multiply (2 + x) * (-3 + x)
2x2 = (2(-3 + x) + x(-3 + x)) + 12
2x2 = ((-3 * 2 + x * 2) + x(-3 + x)) + 12
2x2 = ((-6 + 2x) + x(-3 + x)) + 12
2x2 = (-6 + 2x + (-3 * x + x * x)) + 12
2x2 = (-6 + 2x + (-3x + x2)) + 12

Combine like terms: 2x + -3x = -1x
2x2 = (-6 + -1x + x2) + 12

Reorder the terms:
2x2 = -6 + 12 + -1x + x2

Combine like terms: -6 + 12 = 6
2x2 = 6 + -1x + x2

Solving
2x2 = 6 + -1x + x2

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
(-3 + -1x)(2 + -1x) = 0


Subproblem 1
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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}

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