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

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


Simplifying
3(2 + 5x) = (2 + 5x)(x + 1)
(2 * 3 + 5x * 3) = (2 + 5x)(x + 1)
(6 + 15x) = (2 + 5x)(x + 1)

Reorder the terms:
6 + 15x = (2 + 5x)(1 + x)

Multiply (2 + 5x) * (1 + x)
6 + 15x = (2(1 + x) + 5x * (1 + x))
6 + 15x = ((1 * 2 + x * 2) + 5x * (1 + x))
6 + 15x = ((2 + 2x) + 5x * (1 + x))
6 + 15x = (2 + 2x + (1 * 5x + x * 5x))
6 + 15x = (2 + 2x + (5x + 5x2))

Combine like terms: 2x + 5x = 7x
6 + 15x = (2 + 7x + 5x2)

Solving
6 + 15x = 2 + 7x + 5x2

Solving for variable 'x'.

Reorder the terms:
6 + -2 + 15x + -7x + -5x2 = 2 + 7x + 5x2 + -2 + -7x + -5x2

Combine like terms: 6 + -2 = 4
4 + 15x + -7x + -5x2 = 2 + 7x + 5x2 + -2 + -7x + -5x2

Combine like terms: 15x + -7x = 8x
4 + 8x + -5x2 = 2 + 7x + 5x2 + -2 + -7x + -5x2

Reorder the terms:
4 + 8x + -5x2 = 2 + -2 + 7x + -7x + 5x2 + -5x2

Combine like terms: 2 + -2 = 0
4 + 8x + -5x2 = 0 + 7x + -7x + 5x2 + -5x2
4 + 8x + -5x2 = 7x + -7x + 5x2 + -5x2

Combine like terms: 7x + -7x = 0
4 + 8x + -5x2 = 0 + 5x2 + -5x2
4 + 8x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
4 + 8x + -5x2 = 0

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


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, -0.4}

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