(3x-5)(x^2-4)=10(x+2)

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Solution for (3x-5)(x^2-4)=10(x+2) equation:


Simplifying
(3x + -5)(x2 + -4) = 10(x + 2)

Reorder the terms:
(-5 + 3x)(x2 + -4) = 10(x + 2)

Reorder the terms:
(-5 + 3x)(-4 + x2) = 10(x + 2)

Multiply (-5 + 3x) * (-4 + x2)
(-5(-4 + x2) + 3x * (-4 + x2)) = 10(x + 2)
((-4 * -5 + x2 * -5) + 3x * (-4 + x2)) = 10(x + 2)
((20 + -5x2) + 3x * (-4 + x2)) = 10(x + 2)
(20 + -5x2 + (-4 * 3x + x2 * 3x)) = 10(x + 2)
(20 + -5x2 + (-12x + 3x3)) = 10(x + 2)

Reorder the terms:
(20 + -12x + -5x2 + 3x3) = 10(x + 2)
(20 + -12x + -5x2 + 3x3) = 10(x + 2)

Reorder the terms:
20 + -12x + -5x2 + 3x3 = 10(2 + x)
20 + -12x + -5x2 + 3x3 = (2 * 10 + x * 10)
20 + -12x + -5x2 + 3x3 = (20 + 10x)

Add '-20' to each side of the equation.
20 + -12x + -5x2 + -20 + 3x3 = 20 + -20 + 10x

Reorder the terms:
20 + -20 + -12x + -5x2 + 3x3 = 20 + -20 + 10x

Combine like terms: 20 + -20 = 0
0 + -12x + -5x2 + 3x3 = 20 + -20 + 10x
-12x + -5x2 + 3x3 = 20 + -20 + 10x

Combine like terms: 20 + -20 = 0
-12x + -5x2 + 3x3 = 0 + 10x
-12x + -5x2 + 3x3 = 10x

Solving
-12x + -5x2 + 3x3 = 10x

Solving for variable 'x'.

Reorder the terms:
-12x + -10x + -5x2 + 3x3 = 10x + -10x

Combine like terms: -12x + -10x = -22x
-22x + -5x2 + 3x3 = 10x + -10x

Combine like terms: 10x + -10x = 0
-22x + -5x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-22 + -5x + 3x2) = 0

Factor a trinomial.
x((-2 + -1x)(11 + -3x)) = 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 '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 3
Set the factor '(11 + -3x)' equal to zero and attempt to solve:

Simplifying
11 + -3x = 0

Solving
11 + -3x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3x = 0 + -11
-3x = 0 + -11

Combine like terms: 0 + -11 = -11
-3x = -11

Divide each side by '-3'.
x = 3.666666667

Simplifying
x = 3.666666667
Solution
x = {0, -2, 3.666666667}

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