5(3x^2-2x)=3x-2

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


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

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

Reorder the terms:
-10x + 15x2 = -2 + 3x

Solving
-10x + 15x2 = -2 + 3x

Solving for variable 'x'.

Reorder the terms:
2 + -10x + -3x + 15x2 = -2 + 3x + 2 + -3x

Combine like terms: -10x + -3x = -13x
2 + -13x + 15x2 = -2 + 3x + 2 + -3x

Reorder the terms:
2 + -13x + 15x2 = -2 + 2 + 3x + -3x

Combine like terms: -2 + 2 = 0
2 + -13x + 15x2 = 0 + 3x + -3x
2 + -13x + 15x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
2 + -13x + 15x2 = 0

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


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

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2

Subproblem 2
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
Solution
x = {0.2, 0.6666666667}

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