(x-3)(x+2)=(x+4)(2-x)-14

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Solution for (x-3)(x+2)=(x+4)(2-x)-14 equation:


Simplifying
(x + -3)(x + 2) = (x + 4)(2 + -1x) + -14

Reorder the terms:
(-3 + x)(x + 2) = (x + 4)(2 + -1x) + -14

Reorder the terms:
(-3 + x)(2 + x) = (x + 4)(2 + -1x) + -14

Multiply (-3 + x) * (2 + x)
(-3(2 + x) + x(2 + x)) = (x + 4)(2 + -1x) + -14
((2 * -3 + x * -3) + x(2 + x)) = (x + 4)(2 + -1x) + -14
((-6 + -3x) + x(2 + x)) = (x + 4)(2 + -1x) + -14
(-6 + -3x + (2 * x + x * x)) = (x + 4)(2 + -1x) + -14
(-6 + -3x + (2x + x2)) = (x + 4)(2 + -1x) + -14

Combine like terms: -3x + 2x = -1x
(-6 + -1x + x2) = (x + 4)(2 + -1x) + -14

Reorder the terms:
-6 + -1x + x2 = (4 + x)(2 + -1x) + -14

Multiply (4 + x) * (2 + -1x)
-6 + -1x + x2 = (4(2 + -1x) + x(2 + -1x)) + -14
-6 + -1x + x2 = ((2 * 4 + -1x * 4) + x(2 + -1x)) + -14
-6 + -1x + x2 = ((8 + -4x) + x(2 + -1x)) + -14
-6 + -1x + x2 = (8 + -4x + (2 * x + -1x * x)) + -14
-6 + -1x + x2 = (8 + -4x + (2x + -1x2)) + -14

Combine like terms: -4x + 2x = -2x
-6 + -1x + x2 = (8 + -2x + -1x2) + -14

Reorder the terms:
-6 + -1x + x2 = 8 + -14 + -2x + -1x2

Combine like terms: 8 + -14 = -6
-6 + -1x + x2 = -6 + -2x + -1x2

Add '6' to each side of the equation.
-6 + -1x + 6 + x2 = -6 + -2x + 6 + -1x2

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

Combine like terms: -6 + 6 = 0
0 + -1x + x2 = -6 + -2x + 6 + -1x2
-1x + x2 = -6 + -2x + 6 + -1x2

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

Combine like terms: -6 + 6 = 0
-1x + x2 = 0 + -2x + -1x2
-1x + x2 = -2x + -1x2

Solving
-1x + x2 = -2x + -1x2

Solving for variable 'x'.

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

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

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

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

Combine like terms: -2x + 2x = 0
1x + 2x2 = 0 + -1x2 + x2
1x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
1x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + 2x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {0, -0.5}

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