3(x+5)(x-4)=(x-3)(5x+4)

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Solution for 3(x+5)(x-4)=(x-3)(5x+4) equation:


Simplifying
3(x + 5)(x + -4) = (x + -3)(5x + 4)

Reorder the terms:
3(5 + x)(x + -4) = (x + -3)(5x + 4)

Reorder the terms:
3(5 + x)(-4 + x) = (x + -3)(5x + 4)

Multiply (5 + x) * (-4 + x)
3(5(-4 + x) + x(-4 + x)) = (x + -3)(5x + 4)
3((-4 * 5 + x * 5) + x(-4 + x)) = (x + -3)(5x + 4)
3((-20 + 5x) + x(-4 + x)) = (x + -3)(5x + 4)
3(-20 + 5x + (-4 * x + x * x)) = (x + -3)(5x + 4)
3(-20 + 5x + (-4x + x2)) = (x + -3)(5x + 4)

Combine like terms: 5x + -4x = 1x
3(-20 + 1x + x2) = (x + -3)(5x + 4)
(-20 * 3 + 1x * 3 + x2 * 3) = (x + -3)(5x + 4)
(-60 + 3x + 3x2) = (x + -3)(5x + 4)

Reorder the terms:
-60 + 3x + 3x2 = (-3 + x)(5x + 4)

Reorder the terms:
-60 + 3x + 3x2 = (-3 + x)(4 + 5x)

Multiply (-3 + x) * (4 + 5x)
-60 + 3x + 3x2 = (-3(4 + 5x) + x(4 + 5x))
-60 + 3x + 3x2 = ((4 * -3 + 5x * -3) + x(4 + 5x))
-60 + 3x + 3x2 = ((-12 + -15x) + x(4 + 5x))
-60 + 3x + 3x2 = (-12 + -15x + (4 * x + 5x * x))
-60 + 3x + 3x2 = (-12 + -15x + (4x + 5x2))

Combine like terms: -15x + 4x = -11x
-60 + 3x + 3x2 = (-12 + -11x + 5x2)

Solving
-60 + 3x + 3x2 = -12 + -11x + 5x2

Solving for variable 'x'.

Reorder the terms:
-60 + 12 + 3x + 11x + 3x2 + -5x2 = -12 + -11x + 5x2 + 12 + 11x + -5x2

Combine like terms: -60 + 12 = -48
-48 + 3x + 11x + 3x2 + -5x2 = -12 + -11x + 5x2 + 12 + 11x + -5x2

Combine like terms: 3x + 11x = 14x
-48 + 14x + 3x2 + -5x2 = -12 + -11x + 5x2 + 12 + 11x + -5x2

Combine like terms: 3x2 + -5x2 = -2x2
-48 + 14x + -2x2 = -12 + -11x + 5x2 + 12 + 11x + -5x2

Reorder the terms:
-48 + 14x + -2x2 = -12 + 12 + -11x + 11x + 5x2 + -5x2

Combine like terms: -12 + 12 = 0
-48 + 14x + -2x2 = 0 + -11x + 11x + 5x2 + -5x2
-48 + 14x + -2x2 = -11x + 11x + 5x2 + -5x2

Combine like terms: -11x + 11x = 0
-48 + 14x + -2x2 = 0 + 5x2 + -5x2
-48 + 14x + -2x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-48 + 14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 7x + -1x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-24 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying -24 + 7x + -1x2 = 0 Solving -24 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 24 + -7x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -7x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -7x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -7x + x2 = 0 + -24 -7x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -7x + x2 = -24 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -24 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -24 + 12.25 Combine like terms: -24 + 12.25 = -11.75 12.25 + -7x + x2 = -11.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -11.75 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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