x(x-7)=x(4x+15)

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Solution for x(x-7)=x(4x+15) equation: 


Simplifying
x(x + -7) = x(4x + 15)

Reorder the terms:
x(-7 + x) = x(4x + 15)
(-7 * x + x * x) = x(4x + 15)
(-7x + x2) = x(4x + 15)

Reorder the terms:
-7x + x2 = x(15 + 4x)
-7x + x2 = (15 * x + 4x * x)
-7x + x2 = (15x + 4x2)

Solving
-7x + x2 = 15x + 4x2

Solving for variable 'x'.

Reorder the terms:
-7x + -15x + x2 + -4x2 = 15x + 4x2 + -15x + -4x2

Combine like terms: -7x + -15x = -22x
-22x + x2 + -4x2 = 15x + 4x2 + -15x + -4x2

Combine like terms: x2 + -4x2 = -3x2
-22x + -3x2 = 15x + 4x2 + -15x + -4x2

Reorder the terms:
-22x + -3x2 = 15x + -15x + 4x2 + -4x2

Combine like terms: 15x + -15x = 0
-22x + -3x2 = 0 + 4x2 + -4x2
-22x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-22x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(22 + 3x) = 0

Ignore the factor -1.

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 '(22 + 3x)' equal to zero and attempt to solve:

Simplifying
22 + 3x = 0

Solving
22 + 3x = 0

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

Add '-22' to each side of the equation.
22 + -22 + 3x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 3x = 0 + -22
3x = 0 + -22

Combine like terms: 0 + -22 = -22
3x = -22

Divide each side by '3'.
x = -7.333333333

Simplifying
x = -7.333333333
Solution
x = {0, -7.333333333}

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