x(9x+8)=4x^2-11x+4

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Solution for x(9x+8)=4x^2-11x+4 equation:


Simplifying
x(9x + 8) = 4x2 + -11x + 4

Reorder the terms:
x(8 + 9x) = 4x2 + -11x + 4
(8 * x + 9x * x) = 4x2 + -11x + 4
(8x + 9x2) = 4x2 + -11x + 4

Reorder the terms:
8x + 9x2 = 4 + -11x + 4x2

Solving
8x + 9x2 = 4 + -11x + 4x2

Solving for variable 'x'.

Reorder the terms:
-4 + 8x + 11x + 9x2 + -4x2 = 4 + -11x + 4x2 + -4 + 11x + -4x2

Combine like terms: 8x + 11x = 19x
-4 + 19x + 9x2 + -4x2 = 4 + -11x + 4x2 + -4 + 11x + -4x2

Combine like terms: 9x2 + -4x2 = 5x2
-4 + 19x + 5x2 = 4 + -11x + 4x2 + -4 + 11x + -4x2

Reorder the terms:
-4 + 19x + 5x2 = 4 + -4 + -11x + 11x + 4x2 + -4x2

Combine like terms: 4 + -4 = 0
-4 + 19x + 5x2 = 0 + -11x + 11x + 4x2 + -4x2
-4 + 19x + 5x2 = -11x + 11x + 4x2 + -4x2

Combine like terms: -11x + 11x = 0
-4 + 19x + 5x2 = 0 + 4x2 + -4x2
-4 + 19x + 5x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-4 + 19x + 5x2 = 0

Factor a trinomial.
(-4 + -1x)(1 + -5x) = 0

Subproblem 1

Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 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 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4

Subproblem 2

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

Solution

x = {-4, 0.2}

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