x(3x-5)=(3x+9)(x-7)

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Solution for x(3x-5)=(3x+9)(x-7) equation:


Simplifying
x(3x + -5) = (3x + 9)(x + -7)

Reorder the terms:
x(-5 + 3x) = (3x + 9)(x + -7)
(-5 * x + 3x * x) = (3x + 9)(x + -7)
(-5x + 3x2) = (3x + 9)(x + -7)

Reorder the terms:
-5x + 3x2 = (9 + 3x)(x + -7)

Reorder the terms:
-5x + 3x2 = (9 + 3x)(-7 + x)

Multiply (9 + 3x) * (-7 + x)
-5x + 3x2 = (9(-7 + x) + 3x * (-7 + x))
-5x + 3x2 = ((-7 * 9 + x * 9) + 3x * (-7 + x))
-5x + 3x2 = ((-63 + 9x) + 3x * (-7 + x))
-5x + 3x2 = (-63 + 9x + (-7 * 3x + x * 3x))
-5x + 3x2 = (-63 + 9x + (-21x + 3x2))

Combine like terms: 9x + -21x = -12x
-5x + 3x2 = (-63 + -12x + 3x2)

Add '-3x2' to each side of the equation.
-5x + 3x2 + -3x2 = -63 + -12x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-5x + 0 = -63 + -12x + 3x2 + -3x2
-5x = -63 + -12x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-5x = -63 + -12x + 0
-5x = -63 + -12x

Solving
-5x = -63 + -12x

Solving for variable 'x'.

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

Add '12x' to each side of the equation.
-5x + 12x = -63 + -12x + 12x

Combine like terms: -5x + 12x = 7x
7x = -63 + -12x + 12x

Combine like terms: -12x + 12x = 0
7x = -63 + 0
7x = -63

Divide each side by '7'.
x = -9

Simplifying
x = -9

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