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

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


Simplifying
x2 + 10x + 10 = x(4x + -3)

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

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

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

Solving for variable 'x'.

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

Combine like terms: 10x + 3x = 13x
10 + 13x + x2 + -4x2 = -3x + 4x2 + 3x + -4x2

Combine like terms: x2 + -4x2 = -3x2
10 + 13x + -3x2 = -3x + 4x2 + 3x + -4x2

Reorder the terms:
10 + 13x + -3x2 = -3x + 3x + 4x2 + -4x2

Combine like terms: -3x + 3x = 0
10 + 13x + -3x2 = 0 + 4x2 + -4x2
10 + 13x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
10 + 13x + -3x2 = 0

Factor a trinomial.
(5 + -1x)(2 + 3x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {5, -0.6666666667}

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