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

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


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

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

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

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

Multiply (-1 + x) * (3 + x)
5x + 2x2 = 7x + -1(-1(3 + x) + x(3 + x))
5x + 2x2 = 7x + -1((3 * -1 + x * -1) + x(3 + x))
5x + 2x2 = 7x + -1((-3 + -1x) + x(3 + x))
5x + 2x2 = 7x + -1(-3 + -1x + (3 * x + x * x))
5x + 2x2 = 7x + -1(-3 + -1x + (3x + x2))

Combine like terms: -1x + 3x = 2x
5x + 2x2 = 7x + -1(-3 + 2x + x2)
5x + 2x2 = 7x + (-3 * -1 + 2x * -1 + x2 * -1)
5x + 2x2 = 7x + (3 + -2x + -1x2)

Reorder the terms:
5x + 2x2 = 3 + 7x + -2x + -1x2

Combine like terms: 7x + -2x = 5x
5x + 2x2 = 3 + 5x + -1x2

Add '-5x' to each side of the equation.
5x + -5x + 2x2 = 3 + 5x + -5x + -1x2

Combine like terms: 5x + -5x = 0
0 + 2x2 = 3 + 5x + -5x + -1x2
2x2 = 3 + 5x + -5x + -1x2

Combine like terms: 5x + -5x = 0
2x2 = 3 + 0 + -1x2
2x2 = 3 + -1x2

Solving
2x2 = 3 + -1x2

Solving for variable 'x'.

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

Add 'x2' to each side of the equation.
2x2 + x2 = 3 + -1x2 + x2

Combine like terms: 2x2 + x2 = 3x2
3x2 = 3 + -1x2 + x2

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

Divide each side by '3'.
x2 = 1

Simplifying
x2 = 1

Take the square root of each side:
x = {-1, 1}

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