(5x-6)(x-9)=(4x-3)(x-14)

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Solution for (5x-6)(x-9)=(4x-3)(x-14) equation: 


Simplifying
(5x + -6)(x + -9) = (4x + -3)(x + -14)

Reorder the terms:
(-6 + 5x)(x + -9) = (4x + -3)(x + -14)

Reorder the terms:
(-6 + 5x)(-9 + x) = (4x + -3)(x + -14)

Multiply (-6 + 5x) * (-9 + x)
(-6(-9 + x) + 5x * (-9 + x)) = (4x + -3)(x + -14)
((-9 * -6 + x * -6) + 5x * (-9 + x)) = (4x + -3)(x + -14)
((54 + -6x) + 5x * (-9 + x)) = (4x + -3)(x + -14)
(54 + -6x + (-9 * 5x + x * 5x)) = (4x + -3)(x + -14)
(54 + -6x + (-45x + 5x2)) = (4x + -3)(x + -14)

Combine like terms: -6x + -45x = -51x
(54 + -51x + 5x2) = (4x + -3)(x + -14)

Reorder the terms:
54 + -51x + 5x2 = (-3 + 4x)(x + -14)

Reorder the terms:
54 + -51x + 5x2 = (-3 + 4x)(-14 + x)

Multiply (-3 + 4x) * (-14 + x)
54 + -51x + 5x2 = (-3(-14 + x) + 4x * (-14 + x))
54 + -51x + 5x2 = ((-14 * -3 + x * -3) + 4x * (-14 + x))
54 + -51x + 5x2 = ((42 + -3x) + 4x * (-14 + x))
54 + -51x + 5x2 = (42 + -3x + (-14 * 4x + x * 4x))
54 + -51x + 5x2 = (42 + -3x + (-56x + 4x2))

Combine like terms: -3x + -56x = -59x
54 + -51x + 5x2 = (42 + -59x + 4x2)

Solving
54 + -51x + 5x2 = 42 + -59x + 4x2

Solving for variable 'x'.

Reorder the terms:
54 + -42 + -51x + 59x + 5x2 + -4x2 = 42 + -59x + 4x2 + -42 + 59x + -4x2

Combine like terms: 54 + -42 = 12
12 + -51x + 59x + 5x2 + -4x2 = 42 + -59x + 4x2 + -42 + 59x + -4x2

Combine like terms: -51x + 59x = 8x
12 + 8x + 5x2 + -4x2 = 42 + -59x + 4x2 + -42 + 59x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
12 + 8x + 1x2 = 42 + -59x + 4x2 + -42 + 59x + -4x2

Reorder the terms:
12 + 8x + 1x2 = 42 + -42 + -59x + 59x + 4x2 + -4x2

Combine like terms: 42 + -42 = 0
12 + 8x + 1x2 = 0 + -59x + 59x + 4x2 + -4x2
12 + 8x + 1x2 = -59x + 59x + 4x2 + -4x2

Combine like terms: -59x + 59x = 0
12 + 8x + 1x2 = 0 + 4x2 + -4x2
12 + 8x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
12 + 8x + 1x2 = 0

Factor a trinomial.
(6 + x)(2 + x) = 0


Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {-6, -2}

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