3(x-3)(x+2)=3(x-10)

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Solution for 3(x-3)(x+2)=3(x-10) equation:


Simplifying
3(x + -3)(x + 2) = 3(x + -10)

Reorder the terms:
3(-3 + x)(x + 2) = 3(x + -10)

Reorder the terms:
3(-3 + x)(2 + x) = 3(x + -10)

Multiply (-3 + x) * (2 + x)
3(-3(2 + x) + x(2 + x)) = 3(x + -10)
3((2 * -3 + x * -3) + x(2 + x)) = 3(x + -10)
3((-6 + -3x) + x(2 + x)) = 3(x + -10)
3(-6 + -3x + (2 * x + x * x)) = 3(x + -10)
3(-6 + -3x + (2x + x2)) = 3(x + -10)

Combine like terms: -3x + 2x = -1x
3(-6 + -1x + x2) = 3(x + -10)
(-6 * 3 + -1x * 3 + x2 * 3) = 3(x + -10)
(-18 + -3x + 3x2) = 3(x + -10)

Reorder the terms:
-18 + -3x + 3x2 = 3(-10 + x)
-18 + -3x + 3x2 = (-10 * 3 + x * 3)
-18 + -3x + 3x2 = (-30 + 3x)

Solving
-18 + -3x + 3x2 = -30 + 3x

Solving for variable 'x'.

Reorder the terms:
-18 + 30 + -3x + -3x + 3x2 = -30 + 3x + 30 + -3x

Combine like terms: -18 + 30 = 12
12 + -3x + -3x + 3x2 = -30 + 3x + 30 + -3x

Combine like terms: -3x + -3x = -6x
12 + -6x + 3x2 = -30 + 3x + 30 + -3x

Reorder the terms:
12 + -6x + 3x2 = -30 + 30 + 3x + -3x

Combine like terms: -30 + 30 = 0
12 + -6x + 3x2 = 0 + 3x + -3x
12 + -6x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
12 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -2x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(4 + -2x + x2)' equal to zero and attempt to solve: Simplifying 4 + -2x + x2 = 0 Solving 4 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -2x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -2x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -2x + x2 = 0 + -4 -2x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -2x + x2 = -4 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -4 + 1 Reorder the terms: 1 + -2x + x2 = -4 + 1 Combine like terms: -4 + 1 = -3 1 + -2x + x2 = -3 Factor a perfect square on the left side: (x + -1)(x + -1) = -3 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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