x(3x-3)+x(4x-3)=(7x+6)(x-3)

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Solution for x(3x-3)+x(4x-3)=(7x+6)(x-3) equation: 


Simplifying
x(3x + -3) + x(4x + -3) = (7x + 6)(x + -3)

Reorder the terms:
x(-3 + 3x) + x(4x + -3) = (7x + 6)(x + -3)
(-3 * x + 3x * x) + x(4x + -3) = (7x + 6)(x + -3)
(-3x + 3x2) + x(4x + -3) = (7x + 6)(x + -3)

Reorder the terms:
-3x + 3x2 + x(-3 + 4x) = (7x + 6)(x + -3)
-3x + 3x2 + (-3 * x + 4x * x) = (7x + 6)(x + -3)
-3x + 3x2 + (-3x + 4x2) = (7x + 6)(x + -3)

Reorder the terms:
-3x + -3x + 3x2 + 4x2 = (7x + 6)(x + -3)

Combine like terms: -3x + -3x = -6x
-6x + 3x2 + 4x2 = (7x + 6)(x + -3)

Combine like terms: 3x2 + 4x2 = 7x2
-6x + 7x2 = (7x + 6)(x + -3)

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

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

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

Combine like terms: 6x + -21x = -15x
-6x + 7x2 = (-18 + -15x + 7x2)

Add '-7x2' to each side of the equation.
-6x + 7x2 + -7x2 = -18 + -15x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-6x + 0 = -18 + -15x + 7x2 + -7x2
-6x = -18 + -15x + 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-6x = -18 + -15x + 0
-6x = -18 + -15x

Solving
-6x = -18 + -15x

Solving for variable 'x'.

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

Add '15x' to each side of the equation.
-6x + 15x = -18 + -15x + 15x

Combine like terms: -6x + 15x = 9x
9x = -18 + -15x + 15x

Combine like terms: -15x + 15x = 0
9x = -18 + 0
9x = -18

Divide each side by '9'.
x = -2

Simplifying
x = -2

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