x(x+3)=2(x+3)(x-1)+126

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Solution for x(x+3)=2(x+3)(x-1)+126 equation:


Simplifying
x(x + 3) = 2(x + 3)(x + -1) + 126

Reorder the terms:
x(3 + x) = 2(x + 3)(x + -1) + 126
(3 * x + x * x) = 2(x + 3)(x + -1) + 126
(3x + x2) = 2(x + 3)(x + -1) + 126

Reorder the terms:
3x + x2 = 2(3 + x)(x + -1) + 126

Reorder the terms:
3x + x2 = 2(3 + x)(-1 + x) + 126

Multiply (3 + x) * (-1 + x)
3x + x2 = 2(3(-1 + x) + x(-1 + x)) + 126
3x + x2 = 2((-1 * 3 + x * 3) + x(-1 + x)) + 126
3x + x2 = 2((-3 + 3x) + x(-1 + x)) + 126
3x + x2 = 2(-3 + 3x + (-1 * x + x * x)) + 126
3x + x2 = 2(-3 + 3x + (-1x + x2)) + 126

Combine like terms: 3x + -1x = 2x
3x + x2 = 2(-3 + 2x + x2) + 126
3x + x2 = (-3 * 2 + 2x * 2 + x2 * 2) + 126
3x + x2 = (-6 + 4x + 2x2) + 126

Reorder the terms:
3x + x2 = -6 + 126 + 4x + 2x2

Combine like terms: -6 + 126 = 120
3x + x2 = 120 + 4x + 2x2

Solving
3x + x2 = 120 + 4x + 2x2

Solving for variable 'x'.

Reorder the terms:
-120 + 3x + -4x + x2 + -2x2 = 120 + 4x + 2x2 + -120 + -4x + -2x2

Combine like terms: 3x + -4x = -1x
-120 + -1x + x2 + -2x2 = 120 + 4x + 2x2 + -120 + -4x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-120 + -1x + -1x2 = 120 + 4x + 2x2 + -120 + -4x + -2x2

Reorder the terms:
-120 + -1x + -1x2 = 120 + -120 + 4x + -4x + 2x2 + -2x2

Combine like terms: 120 + -120 = 0
-120 + -1x + -1x2 = 0 + 4x + -4x + 2x2 + -2x2
-120 + -1x + -1x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
-120 + -1x + -1x2 = 0 + 2x2 + -2x2
-120 + -1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-120 + -1x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(120 + x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(120 + x + x2)' equal to zero and attempt to solve: Simplifying 120 + x + x2 = 0 Solving 120 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + x + x2 = 0 + -120 x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 x + x2 = -120 The x term is x. 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. x + 0.25 + x2 = -120 + 0.25 Reorder the terms: 0.25 + x + x2 = -120 + 0.25 Combine like terms: -120 + 0.25 = -119.75 0.25 + x + x2 = -119.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -119.75 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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