(5x+2)(3x-1)=15(x^2+3)-2x

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Solution for (5x+2)(3x-1)=15(x^2+3)-2x equation: 


Simplifying
(5x + 2)(3x + -1) = 15(x2 + 3) + -2x

Reorder the terms:
(2 + 5x)(3x + -1) = 15(x2 + 3) + -2x

Reorder the terms:
(2 + 5x)(-1 + 3x) = 15(x2 + 3) + -2x

Multiply (2 + 5x) * (-1 + 3x)
(2(-1 + 3x) + 5x * (-1 + 3x)) = 15(x2 + 3) + -2x
((-1 * 2 + 3x * 2) + 5x * (-1 + 3x)) = 15(x2 + 3) + -2x
((-2 + 6x) + 5x * (-1 + 3x)) = 15(x2 + 3) + -2x
(-2 + 6x + (-1 * 5x + 3x * 5x)) = 15(x2 + 3) + -2x
(-2 + 6x + (-5x + 15x2)) = 15(x2 + 3) + -2x

Combine like terms: 6x + -5x = 1x
(-2 + 1x + 15x2) = 15(x2 + 3) + -2x

Reorder the terms:
-2 + 1x + 15x2 = 15(3 + x2) + -2x
-2 + 1x + 15x2 = (3 * 15 + x2 * 15) + -2x
-2 + 1x + 15x2 = (45 + 15x2) + -2x

Reorder the terms:
-2 + 1x + 15x2 = 45 + -2x + 15x2

Add '-15x2' to each side of the equation.
-2 + 1x + 15x2 + -15x2 = 45 + -2x + 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-2 + 1x + 0 = 45 + -2x + 15x2 + -15x2
-2 + 1x = 45 + -2x + 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-2 + 1x = 45 + -2x + 0
-2 + 1x = 45 + -2x

Solving
-2 + 1x = 45 + -2x

Solving for variable 'x'.

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

Add '2x' to each side of the equation.
-2 + 1x + 2x = 45 + -2x + 2x

Combine like terms: 1x + 2x = 3x
-2 + 3x = 45 + -2x + 2x

Combine like terms: -2x + 2x = 0
-2 + 3x = 45 + 0
-2 + 3x = 45

Add '2' to each side of the equation.
-2 + 2 + 3x = 45 + 2

Combine like terms: -2 + 2 = 0
0 + 3x = 45 + 2
3x = 45 + 2

Combine like terms: 45 + 2 = 47
3x = 47

Divide each side by '3'.
x = 15.66666667

Simplifying
x = 15.66666667

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