3x(5x-2)-(2x+7)(x-3)=13(x-1)(x+1)-15

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Solution for 3x(5x-2)-(2x+7)(x-3)=13(x-1)(x+1)-15 equation: 


Simplifying
3x(5x + -2) + -1(2x + 7)(x + -3) = 13(x + -1)(x + 1) + -15

Reorder the terms:
3x(-2 + 5x) + -1(2x + 7)(x + -3) = 13(x + -1)(x + 1) + -15
(-2 * 3x + 5x * 3x) + -1(2x + 7)(x + -3) = 13(x + -1)(x + 1) + -15
(-6x + 15x2) + -1(2x + 7)(x + -3) = 13(x + -1)(x + 1) + -15

Reorder the terms:
-6x + 15x2 + -1(7 + 2x)(x + -3) = 13(x + -1)(x + 1) + -15

Reorder the terms:
-6x + 15x2 + -1(7 + 2x)(-3 + x) = 13(x + -1)(x + 1) + -15

Multiply (7 + 2x) * (-3 + x)
-6x + 15x2 + -1(7(-3 + x) + 2x * (-3 + x)) = 13(x + -1)(x + 1) + -15
-6x + 15x2 + -1((-3 * 7 + x * 7) + 2x * (-3 + x)) = 13(x + -1)(x + 1) + -15
-6x + 15x2 + -1((-21 + 7x) + 2x * (-3 + x)) = 13(x + -1)(x + 1) + -15
-6x + 15x2 + -1(-21 + 7x + (-3 * 2x + x * 2x)) = 13(x + -1)(x + 1) + -15
-6x + 15x2 + -1(-21 + 7x + (-6x + 2x2)) = 13(x + -1)(x + 1) + -15

Combine like terms: 7x + -6x = 1x
-6x + 15x2 + -1(-21 + 1x + 2x2) = 13(x + -1)(x + 1) + -15
-6x + 15x2 + (-21 * -1 + 1x * -1 + 2x2 * -1) = 13(x + -1)(x + 1) + -15
-6x + 15x2 + (21 + -1x + -2x2) = 13(x + -1)(x + 1) + -15

Reorder the terms:
21 + -6x + -1x + 15x2 + -2x2 = 13(x + -1)(x + 1) + -15

Combine like terms: -6x + -1x = -7x
21 + -7x + 15x2 + -2x2 = 13(x + -1)(x + 1) + -15

Combine like terms: 15x2 + -2x2 = 13x2
21 + -7x + 13x2 = 13(x + -1)(x + 1) + -15

Reorder the terms:
21 + -7x + 13x2 = 13(-1 + x)(x + 1) + -15

Reorder the terms:
21 + -7x + 13x2 = 13(-1 + x)(1 + x) + -15

Multiply (-1 + x) * (1 + x)
21 + -7x + 13x2 = 13(-1(1 + x) + x(1 + x)) + -15
21 + -7x + 13x2 = 13((1 * -1 + x * -1) + x(1 + x)) + -15
21 + -7x + 13x2 = 13((-1 + -1x) + x(1 + x)) + -15
21 + -7x + 13x2 = 13(-1 + -1x + (1 * x + x * x)) + -15
21 + -7x + 13x2 = 13(-1 + -1x + (1x + x2)) + -15

Combine like terms: -1x + 1x = 0
21 + -7x + 13x2 = 13(-1 + 0 + x2) + -15
21 + -7x + 13x2 = 13(-1 + x2) + -15
21 + -7x + 13x2 = (-1 * 13 + x2 * 13) + -15
21 + -7x + 13x2 = (-13 + 13x2) + -15

Reorder the terms:
21 + -7x + 13x2 = -13 + -15 + 13x2

Combine like terms: -13 + -15 = -28
21 + -7x + 13x2 = -28 + 13x2

Add '-13x2' to each side of the equation.
21 + -7x + 13x2 + -13x2 = -28 + 13x2 + -13x2

Combine like terms: 13x2 + -13x2 = 0
21 + -7x + 0 = -28 + 13x2 + -13x2
21 + -7x = -28 + 13x2 + -13x2

Combine like terms: 13x2 + -13x2 = 0
21 + -7x = -28 + 0
21 + -7x = -28

Solving
21 + -7x = -28

Solving for variable 'x'.

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

Add '-21' to each side of the equation.
21 + -21 + -7x = -28 + -21

Combine like terms: 21 + -21 = 0
0 + -7x = -28 + -21
-7x = -28 + -21

Combine like terms: -28 + -21 = -49
-7x = -49

Divide each side by '-7'.
x = 7

Simplifying
x = 7

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