5x(x-1)+7=4x(x-2)

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Solution for 5x(x-1)+7=4x(x-2) equation: 


Simplifying
5x(x + -1) + 7 = 4x(x + -2)

Reorder the terms:
5x(-1 + x) + 7 = 4x(x + -2)
(-1 * 5x + x * 5x) + 7 = 4x(x + -2)
(-5x + 5x2) + 7 = 4x(x + -2)

Reorder the terms:
7 + -5x + 5x2 = 4x(x + -2)

Reorder the terms:
7 + -5x + 5x2 = 4x(-2 + x)
7 + -5x + 5x2 = (-2 * 4x + x * 4x)
7 + -5x + 5x2 = (-8x + 4x2)

Solving
7 + -5x + 5x2 = -8x + 4x2

Solving for variable 'x'.

Reorder the terms:
7 + -5x + 8x + 5x2 + -4x2 = -8x + 4x2 + 8x + -4x2

Combine like terms: -5x + 8x = 3x
7 + 3x + 5x2 + -4x2 = -8x + 4x2 + 8x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
7 + 3x + 1x2 = -8x + 4x2 + 8x + -4x2

Reorder the terms:
7 + 3x + 1x2 = -8x + 8x + 4x2 + -4x2

Combine like terms: -8x + 8x = 0
7 + 3x + 1x2 = 0 + 4x2 + -4x2
7 + 3x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
7 + 3x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 3x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 3x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x + x2 = 0 + -7
3x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
3x + x2 = -7

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -7 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -7 + 2.25

Combine like terms: -7 + 2.25 = -4.75
2.25 + 3x + x2 = -4.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -4.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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