x(3x-5)+x(4x-2)=(7x+5)(x-2)

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Solution for x(3x-5)+x(4x-2)=(7x+5)(x-2) equation:


Simplifying
x(3x + -5) + x(4x + -2) = (7x + 5)(x + -2)

Reorder the terms:
x(-5 + 3x) + x(4x + -2) = (7x + 5)(x + -2)
(-5 * x + 3x * x) + x(4x + -2) = (7x + 5)(x + -2)
(-5x + 3x2) + x(4x + -2) = (7x + 5)(x + -2)

Reorder the terms:
-5x + 3x2 + x(-2 + 4x) = (7x + 5)(x + -2)
-5x + 3x2 + (-2 * x + 4x * x) = (7x + 5)(x + -2)
-5x + 3x2 + (-2x + 4x2) = (7x + 5)(x + -2)

Reorder the terms:
-5x + -2x + 3x2 + 4x2 = (7x + 5)(x + -2)

Combine like terms: -5x + -2x = -7x
-7x + 3x2 + 4x2 = (7x + 5)(x + -2)

Combine like terms: 3x2 + 4x2 = 7x2
-7x + 7x2 = (7x + 5)(x + -2)

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

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

Multiply (5 + 7x) * (-2 + x)
-7x + 7x2 = (5(-2 + x) + 7x * (-2 + x))
-7x + 7x2 = ((-2 * 5 + x * 5) + 7x * (-2 + x))
-7x + 7x2 = ((-10 + 5x) + 7x * (-2 + x))
-7x + 7x2 = (-10 + 5x + (-2 * 7x + x * 7x))
-7x + 7x2 = (-10 + 5x + (-14x + 7x2))

Combine like terms: 5x + -14x = -9x
-7x + 7x2 = (-10 + -9x + 7x2)

Add '-7x2' to each side of the equation.
-7x + 7x2 + -7x2 = -10 + -9x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-7x + 0 = -10 + -9x + 7x2 + -7x2
-7x = -10 + -9x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-7x = -10 + -9x + 0
-7x = -10 + -9x

Solving
-7x = -10 + -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 = -10 + -9x + 9x

Combine like terms: -7x + 9x = 2x
2x = -10 + -9x + 9x

Combine like terms: -9x + 9x = 0
2x = -10 + 0
2x = -10

Divide each side by '2'.
x = -5

Simplifying
x = -5

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