(x-4)(x+7)=x+x+3x-28

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Solution for (x-4)(x+7)=x+x+3x-28 equation: 


Simplifying
(x + -4)(x + 7) = x + x + 3x + -28

Reorder the terms:
(-4 + x)(x + 7) = x + x + 3x + -28

Reorder the terms:
(-4 + x)(7 + x) = x + x + 3x + -28

Multiply (-4 + x) * (7 + x)
(-4(7 + x) + x(7 + x)) = x + x + 3x + -28
((7 * -4 + x * -4) + x(7 + x)) = x + x + 3x + -28
((-28 + -4x) + x(7 + x)) = x + x + 3x + -28
(-28 + -4x + (7 * x + x * x)) = x + x + 3x + -28
(-28 + -4x + (7x + x2)) = x + x + 3x + -28

Combine like terms: -4x + 7x = 3x
(-28 + 3x + x2) = x + x + 3x + -28

Reorder the terms:
-28 + 3x + x2 = -28 + x + x + 3x

Combine like terms: x + x = 2x
-28 + 3x + x2 = -28 + 2x + 3x

Combine like terms: 2x + 3x = 5x
-28 + 3x + x2 = -28 + 5x

Add '28' to each side of the equation.
-28 + 3x + 28 + x2 = -28 + 28 + 5x

Reorder the terms:
-28 + 28 + 3x + x2 = -28 + 28 + 5x

Combine like terms: -28 + 28 = 0
0 + 3x + x2 = -28 + 28 + 5x
3x + x2 = -28 + 28 + 5x

Combine like terms: -28 + 28 = 0
3x + x2 = 0 + 5x
3x + x2 = 5x

Solving
3x + x2 = 5x

Solving for variable 'x'.

Reorder the terms:
3x + -5x + x2 = 5x + -5x

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

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

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2
Solution
x = {0, 2}

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