2x(4x+11)+36(4x+11)=0

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Solution for 2x(4x+11)+36(4x+11)=0 equation:


Simplifying
2x(4x + 11) + 36(4x + 11) = 0

Reorder the terms:
2x(11 + 4x) + 36(4x + 11) = 0
(11 * 2x + 4x * 2x) + 36(4x + 11) = 0
(22x + 8x2) + 36(4x + 11) = 0

Reorder the terms:
22x + 8x2 + 36(11 + 4x) = 0
22x + 8x2 + (11 * 36 + 4x * 36) = 0
22x + 8x2 + (396 + 144x) = 0

Reorder the terms:
396 + 22x + 144x + 8x2 = 0

Combine like terms: 22x + 144x = 166x
396 + 166x + 8x2 = 0

Solving
396 + 166x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(198 + 83x + 4x2) = 0

Factor a trinomial.
2((18 + x)(11 + 4x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(18 + x)' equal to zero and attempt to solve: Simplifying 18 + x = 0 Solving 18 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + x = 0 + -18 x = 0 + -18 Combine like terms: 0 + -18 = -18 x = -18 Simplifying x = -18

Subproblem 2

Set the factor '(11 + 4x)' equal to zero and attempt to solve: Simplifying 11 + 4x = 0 Solving 11 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 4x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 4x = 0 + -11 4x = 0 + -11 Combine like terms: 0 + -11 = -11 4x = -11 Divide each side by '4'. x = -2.75 Simplifying x = -2.75

Solution

x = {-18, -2.75}

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