4x(x+3)=3x(x+5)+10

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Solution for 4x(x+3)=3x(x+5)+10 equation: 


Simplifying
4x(x + 3) = 3x(x + 5) + 10

Reorder the terms:
4x(3 + x) = 3x(x + 5) + 10
(3 * 4x + x * 4x) = 3x(x + 5) + 10
(12x + 4x2) = 3x(x + 5) + 10

Reorder the terms:
12x + 4x2 = 3x(5 + x) + 10
12x + 4x2 = (5 * 3x + x * 3x) + 10
12x + 4x2 = (15x + 3x2) + 10

Reorder the terms:
12x + 4x2 = 10 + 15x + 3x2

Solving
12x + 4x2 = 10 + 15x + 3x2

Solving for variable 'x'.

Reorder the terms:
-10 + 12x + -15x + 4x2 + -3x2 = 10 + 15x + 3x2 + -10 + -15x + -3x2

Combine like terms: 12x + -15x = -3x
-10 + -3x + 4x2 + -3x2 = 10 + 15x + 3x2 + -10 + -15x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-10 + -3x + 1x2 = 10 + 15x + 3x2 + -10 + -15x + -3x2

Reorder the terms:
-10 + -3x + 1x2 = 10 + -10 + 15x + -15x + 3x2 + -3x2

Combine like terms: 10 + -10 = 0
-10 + -3x + 1x2 = 0 + 15x + -15x + 3x2 + -3x2
-10 + -3x + 1x2 = 15x + -15x + 3x2 + -3x2

Combine like terms: 15x + -15x = 0
-10 + -3x + 1x2 = 0 + 3x2 + -3x2
-10 + -3x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-10 + -3x + 1x2 = 0

Factor a trinomial.
(-2 + -1x)(5 + -1x) = 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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-2, 5}

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