(x+3)(x+5)=x(x-3)-7

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Solution for (x+3)(x+5)=x(x-3)-7 equation: 


Simplifying
(x + 3)(x + 5) = x(x + -3) + -7

Reorder the terms:
(3 + x)(x + 5) = x(x + -3) + -7

Reorder the terms:
(3 + x)(5 + x) = x(x + -3) + -7

Multiply (3 + x) * (5 + x)
(3(5 + x) + x(5 + x)) = x(x + -3) + -7
((5 * 3 + x * 3) + x(5 + x)) = x(x + -3) + -7
((15 + 3x) + x(5 + x)) = x(x + -3) + -7
(15 + 3x + (5 * x + x * x)) = x(x + -3) + -7
(15 + 3x + (5x + x2)) = x(x + -3) + -7

Combine like terms: 3x + 5x = 8x
(15 + 8x + x2) = x(x + -3) + -7

Reorder the terms:
15 + 8x + x2 = x(-3 + x) + -7
15 + 8x + x2 = (-3 * x + x * x) + -7
15 + 8x + x2 = (-3x + x2) + -7

Reorder the terms:
15 + 8x + x2 = -7 + -3x + x2

Add '-1x2' to each side of the equation.
15 + 8x + x2 + -1x2 = -7 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + 8x + 0 = -7 + -3x + x2 + -1x2
15 + 8x = -7 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + 8x = -7 + -3x + 0
15 + 8x = -7 + -3x

Solving
15 + 8x = -7 + -3x

Solving for variable 'x'.

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

Add '3x' to each side of the equation.
15 + 8x + 3x = -7 + -3x + 3x

Combine like terms: 8x + 3x = 11x
15 + 11x = -7 + -3x + 3x

Combine like terms: -3x + 3x = 0
15 + 11x = -7 + 0
15 + 11x = -7

Add '-15' to each side of the equation.
15 + -15 + 11x = -7 + -15

Combine like terms: 15 + -15 = 0
0 + 11x = -7 + -15
11x = -7 + -15

Combine like terms: -7 + -15 = -22
11x = -22

Divide each side by '11'.
x = -2

Simplifying
x = -2

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