(3x+2)(x-3)=15x+10

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Solution for (3x+2)(x-3)=15x+10 equation: 


Simplifying
(3x + 2)(x + -3) = 15x + 10

Reorder the terms:
(2 + 3x)(x + -3) = 15x + 10

Reorder the terms:
(2 + 3x)(-3 + x) = 15x + 10

Multiply (2 + 3x) * (-3 + x)
(2(-3 + x) + 3x * (-3 + x)) = 15x + 10
((-3 * 2 + x * 2) + 3x * (-3 + x)) = 15x + 10
((-6 + 2x) + 3x * (-3 + x)) = 15x + 10
(-6 + 2x + (-3 * 3x + x * 3x)) = 15x + 10
(-6 + 2x + (-9x + 3x2)) = 15x + 10

Combine like terms: 2x + -9x = -7x
(-6 + -7x + 3x2) = 15x + 10

Reorder the terms:
-6 + -7x + 3x2 = 10 + 15x

Solving
-6 + -7x + 3x2 = 10 + 15x

Solving for variable 'x'.

Reorder the terms:
-6 + -10 + -7x + -15x + 3x2 = 10 + 15x + -10 + -15x

Combine like terms: -6 + -10 = -16
-16 + -7x + -15x + 3x2 = 10 + 15x + -10 + -15x

Combine like terms: -7x + -15x = -22x
-16 + -22x + 3x2 = 10 + 15x + -10 + -15x

Reorder the terms:
-16 + -22x + 3x2 = 10 + -10 + 15x + -15x

Combine like terms: 10 + -10 = 0
-16 + -22x + 3x2 = 0 + 15x + -15x
-16 + -22x + 3x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
-16 + -22x + 3x2 = 0

Factor a trinomial.
(-2 + -3x)(8 + -1x) = 0


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

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-0.6666666667, 8}

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