(2x+5)(x-6)=x(2x+3)

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Solution for (2x+5)(x-6)=x(2x+3) equation:


Simplifying
(2x + 5)(x + -6) = x(2x + 3)

Reorder the terms:
(5 + 2x)(x + -6) = x(2x + 3)

Reorder the terms:
(5 + 2x)(-6 + x) = x(2x + 3)

Multiply (5 + 2x) * (-6 + x)
(5(-6 + x) + 2x * (-6 + x)) = x(2x + 3)
((-6 * 5 + x * 5) + 2x * (-6 + x)) = x(2x + 3)
((-30 + 5x) + 2x * (-6 + x)) = x(2x + 3)
(-30 + 5x + (-6 * 2x + x * 2x)) = x(2x + 3)
(-30 + 5x + (-12x + 2x2)) = x(2x + 3)

Combine like terms: 5x + -12x = -7x
(-30 + -7x + 2x2) = x(2x + 3)

Reorder the terms:
-30 + -7x + 2x2 = x(3 + 2x)
-30 + -7x + 2x2 = (3 * x + 2x * x)
-30 + -7x + 2x2 = (3x + 2x2)

Add '-2x2' to each side of the equation.
-30 + -7x + 2x2 + -2x2 = 3x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-30 + -7x + 0 = 3x + 2x2 + -2x2
-30 + -7x = 3x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-30 + -7x = 3x + 0
-30 + -7x = 3x

Solving
-30 + -7x = 3x

Solving for variable 'x'.

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

Add '-3x' to each side of the equation.
-30 + -7x + -3x = 3x + -3x

Combine like terms: -7x + -3x = -10x
-30 + -10x = 3x + -3x

Combine like terms: 3x + -3x = 0
-30 + -10x = 0

Add '30' to each side of the equation.
-30 + 30 + -10x = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -10x = 0 + 30
-10x = 0 + 30

Combine like terms: 0 + 30 = 30
-10x = 30

Divide each side by '-10'.
x = -3

Simplifying
x = -3

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