(3x+1)(x-2)-10=0

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Solution for (3x+1)(x-2)-10=0 equation:


Simplifying
(3x + 1)(x + -2) + -10 = 0

Reorder the terms:
(1 + 3x)(x + -2) + -10 = 0

Reorder the terms:
(1 + 3x)(-2 + x) + -10 = 0

Multiply (1 + 3x) * (-2 + x)
(1(-2 + x) + 3x * (-2 + x)) + -10 = 0
((-2 * 1 + x * 1) + 3x * (-2 + x)) + -10 = 0
((-2 + 1x) + 3x * (-2 + x)) + -10 = 0
(-2 + 1x + (-2 * 3x + x * 3x)) + -10 = 0
(-2 + 1x + (-6x + 3x2)) + -10 = 0

Combine like terms: 1x + -6x = -5x
(-2 + -5x + 3x2) + -10 = 0

Reorder the terms:
-2 + -10 + -5x + 3x2 = 0

Combine like terms: -2 + -10 = -12
-12 + -5x + 3x2 = 0

Solving
-12 + -5x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -3x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1.333333333, 3}

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