5x(x-5)=(4x+6)(x-5)

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Solution for 5x(x-5)=(4x+6)(x-5) equation: 


Simplifying
5x(x + -5) = (4x + 6)(x + -5)

Reorder the terms:
5x(-5 + x) = (4x + 6)(x + -5)
(-5 * 5x + x * 5x) = (4x + 6)(x + -5)
(-25x + 5x2) = (4x + 6)(x + -5)

Reorder the terms:
-25x + 5x2 = (6 + 4x)(x + -5)

Reorder the terms:
-25x + 5x2 = (6 + 4x)(-5 + x)

Multiply (6 + 4x) * (-5 + x)
-25x + 5x2 = (6(-5 + x) + 4x * (-5 + x))
-25x + 5x2 = ((-5 * 6 + x * 6) + 4x * (-5 + x))
-25x + 5x2 = ((-30 + 6x) + 4x * (-5 + x))
-25x + 5x2 = (-30 + 6x + (-5 * 4x + x * 4x))
-25x + 5x2 = (-30 + 6x + (-20x + 4x2))

Combine like terms: 6x + -20x = -14x
-25x + 5x2 = (-30 + -14x + 4x2)

Solving
-25x + 5x2 = -30 + -14x + 4x2

Solving for variable 'x'.

Reorder the terms:
30 + -25x + 14x + 5x2 + -4x2 = -30 + -14x + 4x2 + 30 + 14x + -4x2

Combine like terms: -25x + 14x = -11x
30 + -11x + 5x2 + -4x2 = -30 + -14x + 4x2 + 30 + 14x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
30 + -11x + 1x2 = -30 + -14x + 4x2 + 30 + 14x + -4x2

Reorder the terms:
30 + -11x + 1x2 = -30 + 30 + -14x + 14x + 4x2 + -4x2

Combine like terms: -30 + 30 = 0
30 + -11x + 1x2 = 0 + -14x + 14x + 4x2 + -4x2
30 + -11x + 1x2 = -14x + 14x + 4x2 + -4x2

Combine like terms: -14x + 14x = 0
30 + -11x + 1x2 = 0 + 4x2 + -4x2
30 + -11x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
30 + -11x + 1x2 = 0

Factor a trinomial.
(5 + -1x)(6 + -1x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
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
Solution
x = {5, 6}

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