x(3x-5)+x(3x-3)=(6x+7)(x-3)

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Solution for x(3x-5)+x(3x-3)=(6x+7)(x-3) equation:


Simplifying
x(3x + -5) + x(3x + -3) = (6x + 7)(x + -3)

Reorder the terms:
x(-5 + 3x) + x(3x + -3) = (6x + 7)(x + -3)
(-5 * x + 3x * x) + x(3x + -3) = (6x + 7)(x + -3)
(-5x + 3x2) + x(3x + -3) = (6x + 7)(x + -3)

Reorder the terms:
-5x + 3x2 + x(-3 + 3x) = (6x + 7)(x + -3)
-5x + 3x2 + (-3 * x + 3x * x) = (6x + 7)(x + -3)
-5x + 3x2 + (-3x + 3x2) = (6x + 7)(x + -3)

Reorder the terms:
-5x + -3x + 3x2 + 3x2 = (6x + 7)(x + -3)

Combine like terms: -5x + -3x = -8x
-8x + 3x2 + 3x2 = (6x + 7)(x + -3)

Combine like terms: 3x2 + 3x2 = 6x2
-8x + 6x2 = (6x + 7)(x + -3)

Reorder the terms:
-8x + 6x2 = (7 + 6x)(x + -3)

Reorder the terms:
-8x + 6x2 = (7 + 6x)(-3 + x)

Multiply (7 + 6x) * (-3 + x)
-8x + 6x2 = (7(-3 + x) + 6x * (-3 + x))
-8x + 6x2 = ((-3 * 7 + x * 7) + 6x * (-3 + x))
-8x + 6x2 = ((-21 + 7x) + 6x * (-3 + x))
-8x + 6x2 = (-21 + 7x + (-3 * 6x + x * 6x))
-8x + 6x2 = (-21 + 7x + (-18x + 6x2))

Combine like terms: 7x + -18x = -11x
-8x + 6x2 = (-21 + -11x + 6x2)

Add '-6x2' to each side of the equation.
-8x + 6x2 + -6x2 = -21 + -11x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-8x + 0 = -21 + -11x + 6x2 + -6x2
-8x = -21 + -11x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-8x = -21 + -11x + 0
-8x = -21 + -11x

Solving
-8x = -21 + -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.
-8x + 11x = -21 + -11x + 11x

Combine like terms: -8x + 11x = 3x
3x = -21 + -11x + 11x

Combine like terms: -11x + 11x = 0
3x = -21 + 0
3x = -21

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

Simplifying
x = -7

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