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

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


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

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

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

Solving
10x + 5x2 = -2 + 3x

Solving for variable 'x'.

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

Combine like terms: 10x + -3x = 7x
2 + 7x + 5x2 = -2 + 3x + 2 + -3x

Reorder the terms:
2 + 7x + 5x2 = -2 + 2 + 3x + -3x

Combine like terms: -2 + 2 = 0
2 + 7x + 5x2 = 0 + 3x + -3x
2 + 7x + 5x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
2 + 7x + 5x2 = 0

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


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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1

Subproblem 2
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
Solution
x = {-1, -0.4}

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