(5x+3)(x-6)=(2x-6)(2x-6)

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Solution for (5x+3)(x-6)=(2x-6)(2x-6) equation:


Simplifying
(5x + 3)(x + -6) = (2x + -6)(2x + -6)

Reorder the terms:
(3 + 5x)(x + -6) = (2x + -6)(2x + -6)

Reorder the terms:
(3 + 5x)(-6 + x) = (2x + -6)(2x + -6)

Multiply (3 + 5x) * (-6 + x)
(3(-6 + x) + 5x * (-6 + x)) = (2x + -6)(2x + -6)
((-6 * 3 + x * 3) + 5x * (-6 + x)) = (2x + -6)(2x + -6)
((-18 + 3x) + 5x * (-6 + x)) = (2x + -6)(2x + -6)
(-18 + 3x + (-6 * 5x + x * 5x)) = (2x + -6)(2x + -6)
(-18 + 3x + (-30x + 5x2)) = (2x + -6)(2x + -6)

Combine like terms: 3x + -30x = -27x
(-18 + -27x + 5x2) = (2x + -6)(2x + -6)

Reorder the terms:
-18 + -27x + 5x2 = (-6 + 2x)(2x + -6)

Reorder the terms:
-18 + -27x + 5x2 = (-6 + 2x)(-6 + 2x)

Multiply (-6 + 2x) * (-6 + 2x)
-18 + -27x + 5x2 = (-6(-6 + 2x) + 2x * (-6 + 2x))
-18 + -27x + 5x2 = ((-6 * -6 + 2x * -6) + 2x * (-6 + 2x))
-18 + -27x + 5x2 = ((36 + -12x) + 2x * (-6 + 2x))
-18 + -27x + 5x2 = (36 + -12x + (-6 * 2x + 2x * 2x))
-18 + -27x + 5x2 = (36 + -12x + (-12x + 4x2))

Combine like terms: -12x + -12x = -24x
-18 + -27x + 5x2 = (36 + -24x + 4x2)

Solving
-18 + -27x + 5x2 = 36 + -24x + 4x2

Solving for variable 'x'.

Reorder the terms:
-18 + -36 + -27x + 24x + 5x2 + -4x2 = 36 + -24x + 4x2 + -36 + 24x + -4x2

Combine like terms: -18 + -36 = -54
-54 + -27x + 24x + 5x2 + -4x2 = 36 + -24x + 4x2 + -36 + 24x + -4x2

Combine like terms: -27x + 24x = -3x
-54 + -3x + 5x2 + -4x2 = 36 + -24x + 4x2 + -36 + 24x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
-54 + -3x + 1x2 = 36 + -24x + 4x2 + -36 + 24x + -4x2

Reorder the terms:
-54 + -3x + 1x2 = 36 + -36 + -24x + 24x + 4x2 + -4x2

Combine like terms: 36 + -36 = 0
-54 + -3x + 1x2 = 0 + -24x + 24x + 4x2 + -4x2
-54 + -3x + 1x2 = -24x + 24x + 4x2 + -4x2

Combine like terms: -24x + 24x = 0
-54 + -3x + 1x2 = 0 + 4x2 + -4x2
-54 + -3x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-54 + -3x + 1x2 = 0

Factor a trinomial.
(-6 + -1x)(9 + -1x) = 0


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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-6, 9}

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