5(x+3)=5x(x+3)

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


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

Reorder the terms:
5(3 + x) = 5x(x + 3)
(3 * 5 + x * 5) = 5x(x + 3)
(15 + 5x) = 5x(x + 3)

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

Solving
15 + 5x = 15x + 5x2

Solving for variable 'x'.

Combine like terms: 5x + -15x = -10x
15 + -10x + -5x2 = 15x + 5x2 + -15x + -5x2

Reorder the terms:
15 + -10x + -5x2 = 15x + -15x + 5x2 + -5x2

Combine like terms: 15x + -15x = 0
15 + -10x + -5x2 = 0 + 5x2 + -5x2
15 + -10x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
15 + -10x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(3 + -2x + -1x2) = 0

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

Ignore the factor 5.

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Solution
x = {1, -3}

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