(5x-1)(2x+3)=3x-3

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Solution for (5x-1)(2x+3)=3x-3 equation: 


Simplifying
(5x + -1)(2x + 3) = 3x + -3

Reorder the terms:
(-1 + 5x)(2x + 3) = 3x + -3

Reorder the terms:
(-1 + 5x)(3 + 2x) = 3x + -3

Multiply (-1 + 5x) * (3 + 2x)
(-1(3 + 2x) + 5x * (3 + 2x)) = 3x + -3
((3 * -1 + 2x * -1) + 5x * (3 + 2x)) = 3x + -3
((-3 + -2x) + 5x * (3 + 2x)) = 3x + -3
(-3 + -2x + (3 * 5x + 2x * 5x)) = 3x + -3
(-3 + -2x + (15x + 10x2)) = 3x + -3

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

Reorder the terms:
-3 + 13x + 10x2 = -3 + 3x

Add '3' to each side of the equation.
-3 + 13x + 3 + 10x2 = -3 + 3 + 3x

Reorder the terms:
-3 + 3 + 13x + 10x2 = -3 + 3 + 3x

Combine like terms: -3 + 3 = 0
0 + 13x + 10x2 = -3 + 3 + 3x
13x + 10x2 = -3 + 3 + 3x

Combine like terms: -3 + 3 = 0
13x + 10x2 = 0 + 3x
13x + 10x2 = 3x

Solving
13x + 10x2 = 3x

Solving for variable 'x'.

Reorder the terms:
13x + -3x + 10x2 = 3x + -3x

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

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

Factor out the Greatest Common Factor (GCF), '10x'.
10x(1 + x) = 0

Ignore the factor 10.

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
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
Solution
x = {0, -1}

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