(4x+2)(x+10)=5x+11

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Solution for (4x+2)(x+10)=5x+11 equation:


Simplifying
(4x + 2)(x + 10) = 5x + 11

Reorder the terms:
(2 + 4x)(x + 10) = 5x + 11

Reorder the terms:
(2 + 4x)(10 + x) = 5x + 11

Multiply (2 + 4x) * (10 + x)
(2(10 + x) + 4x * (10 + x)) = 5x + 11
((10 * 2 + x * 2) + 4x * (10 + x)) = 5x + 11
((20 + 2x) + 4x * (10 + x)) = 5x + 11
(20 + 2x + (10 * 4x + x * 4x)) = 5x + 11
(20 + 2x + (40x + 4x2)) = 5x + 11

Combine like terms: 2x + 40x = 42x
(20 + 42x + 4x2) = 5x + 11

Reorder the terms:
20 + 42x + 4x2 = 11 + 5x

Solving
20 + 42x + 4x2 = 11 + 5x

Solving for variable 'x'.

Reorder the terms:
20 + -11 + 42x + -5x + 4x2 = 11 + 5x + -11 + -5x

Combine like terms: 20 + -11 = 9
9 + 42x + -5x + 4x2 = 11 + 5x + -11 + -5x

Combine like terms: 42x + -5x = 37x
9 + 37x + 4x2 = 11 + 5x + -11 + -5x

Reorder the terms:
9 + 37x + 4x2 = 11 + -11 + 5x + -5x

Combine like terms: 11 + -11 = 0
9 + 37x + 4x2 = 0 + 5x + -5x
9 + 37x + 4x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
9 + 37x + 4x2 = 0

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

Subproblem 1

Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9

Subproblem 2

Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25

Solution

x = {-9, -0.25}

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