4x(x-4)=(2x+5)(x-4)

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Solution for 4x(x-4)=(2x+5)(x-4) equation: 


Simplifying
4x(x + -4) = (2x + 5)(x + -4)

Reorder the terms:
4x(-4 + x) = (2x + 5)(x + -4)
(-4 * 4x + x * 4x) = (2x + 5)(x + -4)
(-16x + 4x2) = (2x + 5)(x + -4)

Reorder the terms:
-16x + 4x2 = (5 + 2x)(x + -4)

Reorder the terms:
-16x + 4x2 = (5 + 2x)(-4 + x)

Multiply (5 + 2x) * (-4 + x)
-16x + 4x2 = (5(-4 + x) + 2x * (-4 + x))
-16x + 4x2 = ((-4 * 5 + x * 5) + 2x * (-4 + x))
-16x + 4x2 = ((-20 + 5x) + 2x * (-4 + x))
-16x + 4x2 = (-20 + 5x + (-4 * 2x + x * 2x))
-16x + 4x2 = (-20 + 5x + (-8x + 2x2))

Combine like terms: 5x + -8x = -3x
-16x + 4x2 = (-20 + -3x + 2x2)

Solving
-16x + 4x2 = -20 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
20 + -16x + 3x + 4x2 + -2x2 = -20 + -3x + 2x2 + 20 + 3x + -2x2

Combine like terms: -16x + 3x = -13x
20 + -13x + 4x2 + -2x2 = -20 + -3x + 2x2 + 20 + 3x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
20 + -13x + 2x2 = -20 + -3x + 2x2 + 20 + 3x + -2x2

Reorder the terms:
20 + -13x + 2x2 = -20 + 20 + -3x + 3x + 2x2 + -2x2

Combine like terms: -20 + 20 = 0
20 + -13x + 2x2 = 0 + -3x + 3x + 2x2 + -2x2
20 + -13x + 2x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
20 + -13x + 2x2 = 0 + 2x2 + -2x2
20 + -13x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
20 + -13x + 2x2 = 0

Factor a trinomial.
(5 + -2x)(4 + -1x) = 0


Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2.5, 4}

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