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

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


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

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

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

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

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

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

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

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

Multiply (3 + 7x) * (-2 + x)
-5x + 7x2 = (3(-2 + x) + 7x * (-2 + x))
-5x + 7x2 = ((-2 * 3 + x * 3) + 7x * (-2 + x))
-5x + 7x2 = ((-6 + 3x) + 7x * (-2 + x))
-5x + 7x2 = (-6 + 3x + (-2 * 7x + x * 7x))
-5x + 7x2 = (-6 + 3x + (-14x + 7x2))

Combine like terms: 3x + -14x = -11x
-5x + 7x2 = (-6 + -11x + 7x2)

Add '-7x2' to each side of the equation.
-5x + 7x2 + -7x2 = -6 + -11x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-5x + 0 = -6 + -11x + 7x2 + -7x2
-5x = -6 + -11x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-5x = -6 + -11x + 0
-5x = -6 + -11x

Solving
-5x = -6 + -11x

Solving for variable 'x'.

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

Add '11x' to each side of the equation.
-5x + 11x = -6 + -11x + 11x

Combine like terms: -5x + 11x = 6x
6x = -6 + -11x + 11x

Combine like terms: -11x + 11x = 0
6x = -6 + 0
6x = -6

Divide each side by '6'.
x = -1

Simplifying
x = -1

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