21=-3(x+2)(x-3)

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Solution for 21=-3(x+2)(x-3) equation:


Simplifying
21 = -3(x + 2)(x + -3)

Reorder the terms:
21 = -3(2 + x)(x + -3)

Reorder the terms:
21 = -3(2 + x)(-3 + x)

Multiply (2 + x) * (-3 + x)
21 = -3(2(-3 + x) + x(-3 + x))
21 = -3((-3 * 2 + x * 2) + x(-3 + x))
21 = -3((-6 + 2x) + x(-3 + x))
21 = -3(-6 + 2x + (-3 * x + x * x))
21 = -3(-6 + 2x + (-3x + x2))

Combine like terms: 2x + -3x = -1x
21 = -3(-6 + -1x + x2)
21 = (-6 * -3 + -1x * -3 + x2 * -3)
21 = (18 + 3x + -3x2)

Solving
21 = 18 + 3x + -3x2

Solving for variable 'x'.

Combine like terms: 21 + -18 = 3
3 + -3x + 3x2 = 18 + 3x + -3x2 + -18 + -3x + 3x2

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

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

Combine like terms: 3x + -3x = 0
3 + -3x + 3x2 = 0 + -3x2 + 3x2
3 + -3x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
3 + -3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -1x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
1 + -1x + x2 = 0

Solving
1 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1x + x2 = 0 + -1

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

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

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -1 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + -1x + x2 = -0.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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