x(2x-5)+x(2x-2)=(4x+7)(x-4)

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Solution for x(2x-5)+x(2x-2)=(4x+7)(x-4) equation: 


Simplifying
x(2x + -5) + x(2x + -2) = (4x + 7)(x + -4)

Reorder the terms:
x(-5 + 2x) + x(2x + -2) = (4x + 7)(x + -4)
(-5 * x + 2x * x) + x(2x + -2) = (4x + 7)(x + -4)
(-5x + 2x2) + x(2x + -2) = (4x + 7)(x + -4)

Reorder the terms:
-5x + 2x2 + x(-2 + 2x) = (4x + 7)(x + -4)
-5x + 2x2 + (-2 * x + 2x * x) = (4x + 7)(x + -4)
-5x + 2x2 + (-2x + 2x2) = (4x + 7)(x + -4)

Reorder the terms:
-5x + -2x + 2x2 + 2x2 = (4x + 7)(x + -4)

Combine like terms: -5x + -2x = -7x
-7x + 2x2 + 2x2 = (4x + 7)(x + -4)

Combine like terms: 2x2 + 2x2 = 4x2
-7x + 4x2 = (4x + 7)(x + -4)

Reorder the terms:
-7x + 4x2 = (7 + 4x)(x + -4)

Reorder the terms:
-7x + 4x2 = (7 + 4x)(-4 + x)

Multiply (7 + 4x) * (-4 + x)
-7x + 4x2 = (7(-4 + x) + 4x * (-4 + x))
-7x + 4x2 = ((-4 * 7 + x * 7) + 4x * (-4 + x))
-7x + 4x2 = ((-28 + 7x) + 4x * (-4 + x))
-7x + 4x2 = (-28 + 7x + (-4 * 4x + x * 4x))
-7x + 4x2 = (-28 + 7x + (-16x + 4x2))

Combine like terms: 7x + -16x = -9x
-7x + 4x2 = (-28 + -9x + 4x2)

Add '-4x2' to each side of the equation.
-7x + 4x2 + -4x2 = -28 + -9x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-7x + 0 = -28 + -9x + 4x2 + -4x2
-7x = -28 + -9x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-7x = -28 + -9x + 0
-7x = -28 + -9x

Solving
-7x = -28 + -9x

Solving for variable 'x'.

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

Add '9x' to each side of the equation.
-7x + 9x = -28 + -9x + 9x

Combine like terms: -7x + 9x = 2x
2x = -28 + -9x + 9x

Combine like terms: -9x + 9x = 0
2x = -28 + 0
2x = -28

Divide each side by '2'.
x = -14

Simplifying
x = -14

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