(x-1)(4x+5)=(2x-3)(2x-3)

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Solution for (x-1)(4x+5)=(2x-3)(2x-3) equation: 


Simplifying
(x + -1)(4x + 5) = (2x + -3)(2x + -3)

Reorder the terms:
(-1 + x)(4x + 5) = (2x + -3)(2x + -3)

Reorder the terms:
(-1 + x)(5 + 4x) = (2x + -3)(2x + -3)

Multiply (-1 + x) * (5 + 4x)
(-1(5 + 4x) + x(5 + 4x)) = (2x + -3)(2x + -3)
((5 * -1 + 4x * -1) + x(5 + 4x)) = (2x + -3)(2x + -3)
((-5 + -4x) + x(5 + 4x)) = (2x + -3)(2x + -3)
(-5 + -4x + (5 * x + 4x * x)) = (2x + -3)(2x + -3)
(-5 + -4x + (5x + 4x2)) = (2x + -3)(2x + -3)

Combine like terms: -4x + 5x = 1x
(-5 + 1x + 4x2) = (2x + -3)(2x + -3)

Reorder the terms:
-5 + 1x + 4x2 = (-3 + 2x)(2x + -3)

Reorder the terms:
-5 + 1x + 4x2 = (-3 + 2x)(-3 + 2x)

Multiply (-3 + 2x) * (-3 + 2x)
-5 + 1x + 4x2 = (-3(-3 + 2x) + 2x * (-3 + 2x))
-5 + 1x + 4x2 = ((-3 * -3 + 2x * -3) + 2x * (-3 + 2x))
-5 + 1x + 4x2 = ((9 + -6x) + 2x * (-3 + 2x))
-5 + 1x + 4x2 = (9 + -6x + (-3 * 2x + 2x * 2x))
-5 + 1x + 4x2 = (9 + -6x + (-6x + 4x2))

Combine like terms: -6x + -6x = -12x
-5 + 1x + 4x2 = (9 + -12x + 4x2)

Add '-4x2' to each side of the equation.
-5 + 1x + 4x2 + -4x2 = 9 + -12x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-5 + 1x + 0 = 9 + -12x + 4x2 + -4x2
-5 + 1x = 9 + -12x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-5 + 1x = 9 + -12x + 0
-5 + 1x = 9 + -12x

Solving
-5 + 1x = 9 + -12x

Solving for variable 'x'.

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

Add '12x' to each side of the equation.
-5 + 1x + 12x = 9 + -12x + 12x

Combine like terms: 1x + 12x = 13x
-5 + 13x = 9 + -12x + 12x

Combine like terms: -12x + 12x = 0
-5 + 13x = 9 + 0
-5 + 13x = 9

Add '5' to each side of the equation.
-5 + 5 + 13x = 9 + 5

Combine like terms: -5 + 5 = 0
0 + 13x = 9 + 5
13x = 9 + 5

Combine like terms: 9 + 5 = 14
13x = 14

Divide each side by '13'.
x = 1.076923077

Simplifying
x = 1.076923077

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