4x(x+4)=10(x+1)

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


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

Reorder the terms:
4x(4 + x) = 10(x + 1)
(4 * 4x + x * 4x) = 10(x + 1)
(16x + 4x2) = 10(x + 1)

Reorder the terms:
16x + 4x2 = 10(1 + x)
16x + 4x2 = (1 * 10 + x * 10)
16x + 4x2 = (10 + 10x)

Solving
16x + 4x2 = 10 + 10x

Solving for variable 'x'.

Reorder the terms:
-10 + 16x + -10x + 4x2 = 10 + 10x + -10 + -10x

Combine like terms: 16x + -10x = 6x
-10 + 6x + 4x2 = 10 + 10x + -10 + -10x

Reorder the terms:
-10 + 6x + 4x2 = 10 + -10 + 10x + -10x

Combine like terms: 10 + -10 = 0
-10 + 6x + 4x2 = 0 + 10x + -10x
-10 + 6x + 4x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-10 + 6x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 3x + 2x2) = 0

Factor a trinomial.
2((-5 + -2x)(1 + -1x)) = 0

Ignore the factor 2.

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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-2.5, 1}

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