5(2x-1)(x+3)+4x-2=10(x+2)(x-3)+2

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Solution for 5(2x-1)(x+3)+4x-2=10(x+2)(x-3)+2 equation:


Simplifying
5(2x + -1)(x + 3) + 4x + -2 = 10(x + 2)(x + -3) + 2

Reorder the terms:
5(-1 + 2x)(x + 3) + 4x + -2 = 10(x + 2)(x + -3) + 2

Reorder the terms:
5(-1 + 2x)(3 + x) + 4x + -2 = 10(x + 2)(x + -3) + 2

Multiply (-1 + 2x) * (3 + x)
5(-1(3 + x) + 2x * (3 + x)) + 4x + -2 = 10(x + 2)(x + -3) + 2
5((3 * -1 + x * -1) + 2x * (3 + x)) + 4x + -2 = 10(x + 2)(x + -3) + 2
5((-3 + -1x) + 2x * (3 + x)) + 4x + -2 = 10(x + 2)(x + -3) + 2
5(-3 + -1x + (3 * 2x + x * 2x)) + 4x + -2 = 10(x + 2)(x + -3) + 2
5(-3 + -1x + (6x + 2x2)) + 4x + -2 = 10(x + 2)(x + -3) + 2

Combine like terms: -1x + 6x = 5x
5(-3 + 5x + 2x2) + 4x + -2 = 10(x + 2)(x + -3) + 2
(-3 * 5 + 5x * 5 + 2x2 * 5) + 4x + -2 = 10(x + 2)(x + -3) + 2
(-15 + 25x + 10x2) + 4x + -2 = 10(x + 2)(x + -3) + 2

Reorder the terms:
-15 + -2 + 25x + 4x + 10x2 = 10(x + 2)(x + -3) + 2

Combine like terms: -15 + -2 = -17
-17 + 25x + 4x + 10x2 = 10(x + 2)(x + -3) + 2

Combine like terms: 25x + 4x = 29x
-17 + 29x + 10x2 = 10(x + 2)(x + -3) + 2

Reorder the terms:
-17 + 29x + 10x2 = 10(2 + x)(x + -3) + 2

Reorder the terms:
-17 + 29x + 10x2 = 10(2 + x)(-3 + x) + 2

Multiply (2 + x) * (-3 + x)
-17 + 29x + 10x2 = 10(2(-3 + x) + x(-3 + x)) + 2
-17 + 29x + 10x2 = 10((-3 * 2 + x * 2) + x(-3 + x)) + 2
-17 + 29x + 10x2 = 10((-6 + 2x) + x(-3 + x)) + 2
-17 + 29x + 10x2 = 10(-6 + 2x + (-3 * x + x * x)) + 2
-17 + 29x + 10x2 = 10(-6 + 2x + (-3x + x2)) + 2

Combine like terms: 2x + -3x = -1x
-17 + 29x + 10x2 = 10(-6 + -1x + x2) + 2
-17 + 29x + 10x2 = (-6 * 10 + -1x * 10 + x2 * 10) + 2
-17 + 29x + 10x2 = (-60 + -10x + 10x2) + 2

Reorder the terms:
-17 + 29x + 10x2 = -60 + 2 + -10x + 10x2

Combine like terms: -60 + 2 = -58
-17 + 29x + 10x2 = -58 + -10x + 10x2

Add '-10x2' to each side of the equation.
-17 + 29x + 10x2 + -10x2 = -58 + -10x + 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-17 + 29x + 0 = -58 + -10x + 10x2 + -10x2
-17 + 29x = -58 + -10x + 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-17 + 29x = -58 + -10x + 0
-17 + 29x = -58 + -10x

Solving
-17 + 29x = -58 + -10x

Solving for variable 'x'.

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

Add '10x' to each side of the equation.
-17 + 29x + 10x = -58 + -10x + 10x

Combine like terms: 29x + 10x = 39x
-17 + 39x = -58 + -10x + 10x

Combine like terms: -10x + 10x = 0
-17 + 39x = -58 + 0
-17 + 39x = -58

Add '17' to each side of the equation.
-17 + 17 + 39x = -58 + 17

Combine like terms: -17 + 17 = 0
0 + 39x = -58 + 17
39x = -58 + 17

Combine like terms: -58 + 17 = -41
39x = -41

Divide each side by '39'.
x = -1.051282051

Simplifying
x = -1.051282051

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