23x-5x(3x+2)=2x+2

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Solution for 23x-5x(3x+2)=2x+2 equation: 


Simplifying
23x + -5x(3x + 2) = 2x + 2

Reorder the terms:
23x + -5x(2 + 3x) = 2x + 2
23x + (2 * -5x + 3x * -5x) = 2x + 2
23x + (-10x + -15x2) = 2x + 2

Combine like terms: 23x + -10x = 13x
13x + -15x2 = 2x + 2

Reorder the terms:
13x + -15x2 = 2 + 2x

Solving
13x + -15x2 = 2 + 2x

Solving for variable 'x'.

Reorder the terms:
-2 + 13x + -2x + -15x2 = 2 + 2x + -2 + -2x

Combine like terms: 13x + -2x = 11x
-2 + 11x + -15x2 = 2 + 2x + -2 + -2x

Reorder the terms:
-2 + 11x + -15x2 = 2 + -2 + 2x + -2x

Combine like terms: 2 + -2 = 0
-2 + 11x + -15x2 = 0 + 2x + -2x
-2 + 11x + -15x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-2 + 11x + -15x2 = 0

Factor a trinomial.
(-2 + 5x)(1 + -3x) = 0


Subproblem 1
Set the factor '(-2 + 5x)' equal to zero and attempt to solve:

Simplifying
-2 + 5x = 0

Solving
-2 + 5x = 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 + 5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5x = 0 + 2
5x = 0 + 2

Combine like terms: 0 + 2 = 2
5x = 2

Divide each side by '5'.
x = 0.4

Simplifying
x = 0.4

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0.4, 0.3333333333}

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