(5x+6)(x+6)=(x+10)(4x+3)

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Solution for (5x+6)(x+6)=(x+10)(4x+3) equation: 


Simplifying
(5x + 6)(x + 6) = (x + 10)(4x + 3)

Reorder the terms:
(6 + 5x)(x + 6) = (x + 10)(4x + 3)

Reorder the terms:
(6 + 5x)(6 + x) = (x + 10)(4x + 3)

Multiply (6 + 5x) * (6 + x)
(6(6 + x) + 5x * (6 + x)) = (x + 10)(4x + 3)
((6 * 6 + x * 6) + 5x * (6 + x)) = (x + 10)(4x + 3)
((36 + 6x) + 5x * (6 + x)) = (x + 10)(4x + 3)
(36 + 6x + (6 * 5x + x * 5x)) = (x + 10)(4x + 3)
(36 + 6x + (30x + 5x2)) = (x + 10)(4x + 3)

Combine like terms: 6x + 30x = 36x
(36 + 36x + 5x2) = (x + 10)(4x + 3)

Reorder the terms:
36 + 36x + 5x2 = (10 + x)(4x + 3)

Reorder the terms:
36 + 36x + 5x2 = (10 + x)(3 + 4x)

Multiply (10 + x) * (3 + 4x)
36 + 36x + 5x2 = (10(3 + 4x) + x(3 + 4x))
36 + 36x + 5x2 = ((3 * 10 + 4x * 10) + x(3 + 4x))
36 + 36x + 5x2 = ((30 + 40x) + x(3 + 4x))
36 + 36x + 5x2 = (30 + 40x + (3 * x + 4x * x))
36 + 36x + 5x2 = (30 + 40x + (3x + 4x2))

Combine like terms: 40x + 3x = 43x
36 + 36x + 5x2 = (30 + 43x + 4x2)

Solving
36 + 36x + 5x2 = 30 + 43x + 4x2

Solving for variable 'x'.

Reorder the terms:
36 + -30 + 36x + -43x + 5x2 + -4x2 = 30 + 43x + 4x2 + -30 + -43x + -4x2

Combine like terms: 36 + -30 = 6
6 + 36x + -43x + 5x2 + -4x2 = 30 + 43x + 4x2 + -30 + -43x + -4x2

Combine like terms: 36x + -43x = -7x
6 + -7x + 5x2 + -4x2 = 30 + 43x + 4x2 + -30 + -43x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
6 + -7x + 1x2 = 30 + 43x + 4x2 + -30 + -43x + -4x2

Reorder the terms:
6 + -7x + 1x2 = 30 + -30 + 43x + -43x + 4x2 + -4x2

Combine like terms: 30 + -30 = 0
6 + -7x + 1x2 = 0 + 43x + -43x + 4x2 + -4x2
6 + -7x + 1x2 = 43x + -43x + 4x2 + -4x2

Combine like terms: 43x + -43x = 0
6 + -7x + 1x2 = 0 + 4x2 + -4x2
6 + -7x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + -7x + 1x2 = 0

Factor a trinomial.
(1 + -1x)(6 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {1, 6}

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