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

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


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

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

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

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

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

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

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

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

Multiply (7 + 7x) * (-3 + x)
-7x + 7x2 = (7(-3 + x) + 7x * (-3 + x))
-7x + 7x2 = ((-3 * 7 + x * 7) + 7x * (-3 + x))
-7x + 7x2 = ((-21 + 7x) + 7x * (-3 + x))
-7x + 7x2 = (-21 + 7x + (-3 * 7x + x * 7x))
-7x + 7x2 = (-21 + 7x + (-21x + 7x2))

Combine like terms: 7x + -21x = -14x
-7x + 7x2 = (-21 + -14x + 7x2)

Add '-7x2' to each side of the equation.
-7x + 7x2 + -7x2 = -21 + -14x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-7x + 0 = -21 + -14x + 7x2 + -7x2
-7x = -21 + -14x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-7x = -21 + -14x + 0
-7x = -21 + -14x

Solving
-7x = -21 + -14x

Solving for variable 'x'.

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

Add '14x' to each side of the equation.
-7x + 14x = -21 + -14x + 14x

Combine like terms: -7x + 14x = 7x
7x = -21 + -14x + 14x

Combine like terms: -14x + 14x = 0
7x = -21 + 0
7x = -21

Divide each side by '7'.
x = -3

Simplifying
x = -3

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