4x(x+1)-5=10

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Solution for 4x(x+1)-5=10 equation:


Simplifying
4x(x + 1) + -5 = 10

Reorder the terms:
4x(1 + x) + -5 = 10
(1 * 4x + x * 4x) + -5 = 10
(4x + 4x2) + -5 = 10

Reorder the terms:
-5 + 4x + 4x2 = 10

Solving
-5 + 4x + 4x2 = 10

Solving for variable 'x'.

Reorder the terms:
-5 + -10 + 4x + 4x2 = 10 + -10

Combine like terms: -5 + -10 = -15
-15 + 4x + 4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-15 + 4x + 4x2 = 0

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

Subproblem 1

Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5

Subproblem 2

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Solution

x = {-2.5, 1.5}

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