27x(x-1)=-13x^2+7

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Solution for 27x(x-1)=-13x^2+7 equation: 


Simplifying
27x(x + -1) = -13x2 + 7

Reorder the terms:
27x(-1 + x) = -13x2 + 7
(-1 * 27x + x * 27x) = -13x2 + 7
(-27x + 27x2) = -13x2 + 7

Reorder the terms:
-27x + 27x2 = 7 + -13x2

Solving
-27x + 27x2 = 7 + -13x2

Solving for variable 'x'.

Reorder the terms:
-7 + -27x + 27x2 + 13x2 = 7 + -13x2 + -7 + 13x2

Combine like terms: 27x2 + 13x2 = 40x2
-7 + -27x + 40x2 = 7 + -13x2 + -7 + 13x2

Reorder the terms:
-7 + -27x + 40x2 = 7 + -7 + -13x2 + 13x2

Combine like terms: 7 + -7 = 0
-7 + -27x + 40x2 = 0 + -13x2 + 13x2
-7 + -27x + 40x2 = -13x2 + 13x2

Combine like terms: -13x2 + 13x2 = 0
-7 + -27x + 40x2 = 0

Factor a trinomial.
(-1 + -5x)(7 + -8x) = 0


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

Simplifying
-1 + -5x = 0

Solving
-1 + -5x = 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 + -5x = 0 + 1

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

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

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2

Subproblem 2
Set the factor '(7 + -8x)' equal to zero and attempt to solve:

Simplifying
7 + -8x = 0

Solving
7 + -8x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -8x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8x = 0 + -7
-8x = 0 + -7

Combine like terms: 0 + -7 = -7
-8x = -7

Divide each side by '-8'.
x = 0.875

Simplifying
x = 0.875
Solution
x = {-0.2, 0.875}

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