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

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


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

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

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

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

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

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

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

Multiply (3 + 2x) * (-4 + x)
-5 + 3x + 2x2 = (3(-4 + x) + 2x * (-4 + x))
-5 + 3x + 2x2 = ((-4 * 3 + x * 3) + 2x * (-4 + x))
-5 + 3x + 2x2 = ((-12 + 3x) + 2x * (-4 + x))
-5 + 3x + 2x2 = (-12 + 3x + (-4 * 2x + x * 2x))
-5 + 3x + 2x2 = (-12 + 3x + (-8x + 2x2))

Combine like terms: 3x + -8x = -5x
-5 + 3x + 2x2 = (-12 + -5x + 2x2)

Add '-2x2' to each side of the equation.
-5 + 3x + 2x2 + -2x2 = -12 + -5x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5 + 3x + 0 = -12 + -5x + 2x2 + -2x2
-5 + 3x = -12 + -5x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5 + 3x = -12 + -5x + 0
-5 + 3x = -12 + -5x

Solving
-5 + 3x = -12 + -5x

Solving for variable 'x'.

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

Add '5x' to each side of the equation.
-5 + 3x + 5x = -12 + -5x + 5x

Combine like terms: 3x + 5x = 8x
-5 + 8x = -12 + -5x + 5x

Combine like terms: -5x + 5x = 0
-5 + 8x = -12 + 0
-5 + 8x = -12

Add '5' to each side of the equation.
-5 + 5 + 8x = -12 + 5

Combine like terms: -5 + 5 = 0
0 + 8x = -12 + 5
8x = -12 + 5

Combine like terms: -12 + 5 = -7
8x = -7

Divide each side by '8'.
x = -0.875

Simplifying
x = -0.875

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