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

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


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

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

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

Multiply (-1 + 4x) * (2 + x)
(-1(2 + x) + 4x * (2 + x)) = x(2x + -3) + -10
((2 * -1 + x * -1) + 4x * (2 + x)) = x(2x + -3) + -10
((-2 + -1x) + 4x * (2 + x)) = x(2x + -3) + -10
(-2 + -1x + (2 * 4x + x * 4x)) = x(2x + -3) + -10
(-2 + -1x + (8x + 4x2)) = x(2x + -3) + -10

Combine like terms: -1x + 8x = 7x
(-2 + 7x + 4x2) = x(2x + -3) + -10

Reorder the terms:
-2 + 7x + 4x2 = x(-3 + 2x) + -10
-2 + 7x + 4x2 = (-3 * x + 2x * x) + -10
-2 + 7x + 4x2 = (-3x + 2x2) + -10

Reorder the terms:
-2 + 7x + 4x2 = -10 + -3x + 2x2

Solving
-2 + 7x + 4x2 = -10 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-2 + 10 + 7x + 3x + 4x2 + -2x2 = -10 + -3x + 2x2 + 10 + 3x + -2x2

Combine like terms: -2 + 10 = 8
8 + 7x + 3x + 4x2 + -2x2 = -10 + -3x + 2x2 + 10 + 3x + -2x2

Combine like terms: 7x + 3x = 10x
8 + 10x + 4x2 + -2x2 = -10 + -3x + 2x2 + 10 + 3x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
8 + 10x + 2x2 = -10 + -3x + 2x2 + 10 + 3x + -2x2

Reorder the terms:
8 + 10x + 2x2 = -10 + 10 + -3x + 3x + 2x2 + -2x2

Combine like terms: -10 + 10 = 0
8 + 10x + 2x2 = 0 + -3x + 3x + 2x2 + -2x2
8 + 10x + 2x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
8 + 10x + 2x2 = 0 + 2x2 + -2x2
8 + 10x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
8 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 5x + x2) = 0

Factor a trinomial.
2((4 + x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-4, -1}

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