(5x+1)(2x-3)=(10x-3)(x+1)

Solution for (5x+1)(2x-3)=(10x-3)(x+1) equation:

Simplifying
(5x + 1)(2x + -3) = (10x + -3)(x + 1)

Reorder the terms:
(1 + 5x)(2x + -3) = (10x + -3)(x + 1)

Reorder the terms:
(1 + 5x)(-3 + 2x) = (10x + -3)(x + 1)

Multiply (1 + 5x) * (-3 + 2x)
(1(-3 + 2x) + 5x * (-3 + 2x)) = (10x + -3)(x + 1)
((-3 * 1 + 2x * 1) + 5x * (-3 + 2x)) = (10x + -3)(x + 1)
((-3 + 2x) + 5x * (-3 + 2x)) = (10x + -3)(x + 1)
(-3 + 2x + (-3 * 5x + 2x * 5x)) = (10x + -3)(x + 1)
(-3 + 2x + (-15x + 10x2)) = (10x + -3)(x + 1)

Combine like terms: 2x + -15x = -13x
(-3 + -13x + 10x2) = (10x + -3)(x + 1)

Reorder the terms:
-3 + -13x + 10x2 = (-3 + 10x)(x + 1)

Reorder the terms:
-3 + -13x + 10x2 = (-3 + 10x)(1 + x)

Multiply (-3 + 10x) * (1 + x)
-3 + -13x + 10x2 = (-3(1 + x) + 10x * (1 + x))
-3 + -13x + 10x2 = ((1 * -3 + x * -3) + 10x * (1 + x))
-3 + -13x + 10x2 = ((-3 + -3x) + 10x * (1 + x))
-3 + -13x + 10x2 = (-3 + -3x + (1 * 10x + x * 10x))
-3 + -13x + 10x2 = (-3 + -3x + (10x + 10x2))

Combine like terms: -3x + 10x = 7x
-3 + -13x + 10x2 = (-3 + 7x + 10x2)

Add '3' to each side of the equation.
-3 + -13x + 3 + 10x2 = -3 + 7x + 3 + 10x2

Reorder the terms:
-3 + 3 + -13x + 10x2 = -3 + 7x + 3 + 10x2

Combine like terms: -3 + 3 = 0
0 + -13x + 10x2 = -3 + 7x + 3 + 10x2
-13x + 10x2 = -3 + 7x + 3 + 10x2

Reorder the terms:
-13x + 10x2 = -3 + 3 + 7x + 10x2

Combine like terms: -3 + 3 = 0
-13x + 10x2 = 0 + 7x + 10x2
-13x + 10x2 = 7x + 10x2

Add '-10x2' to each side of the equation.
-13x + 10x2 + -10x2 = 7x + 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-13x + 0 = 7x + 10x2 + -10x2
-13x = 7x + 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-13x = 7x + 0
-13x = 7x

Solving
-13x = 7x

Solving for variable 'x'.

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

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

Combine like terms: -13x + -7x = -20x
-20x = 7x + -7x

Combine like terms: 7x + -7x = 0
-20x = 0

Divide each side by '-20'.
x = 0.0

Simplifying
x = 0.0