4x(x+5)-(3x-5)(3x+5)=54-(2x-7)(2x-7)

Solution for 4x(x+5)-(3x-5)(3x+5)=54-(2x-7)(2x-7) equation:

Simplifying
4x(x + 5) + -1(3x + -5)(3x + 5) = 54 + -1(2x + -7)(2x + -7)

Reorder the terms:
4x(5 + x) + -1(3x + -5)(3x + 5) = 54 + -1(2x + -7)(2x + -7)
(5 * 4x + x * 4x) + -1(3x + -5)(3x + 5) = 54 + -1(2x + -7)(2x + -7)
(20x + 4x2) + -1(3x + -5)(3x + 5) = 54 + -1(2x + -7)(2x + -7)

Reorder the terms:
20x + 4x2 + -1(-5 + 3x)(3x + 5) = 54 + -1(2x + -7)(2x + -7)

Reorder the terms:
20x + 4x2 + -1(-5 + 3x)(5 + 3x) = 54 + -1(2x + -7)(2x + -7)

Multiply (-5 + 3x) * (5 + 3x)
20x + 4x2 + -1(-5(5 + 3x) + 3x * (5 + 3x)) = 54 + -1(2x + -7)(2x + -7)
20x + 4x2 + -1((5 * -5 + 3x * -5) + 3x * (5 + 3x)) = 54 + -1(2x + -7)(2x + -7)
20x + 4x2 + -1((-25 + -15x) + 3x * (5 + 3x)) = 54 + -1(2x + -7)(2x + -7)
20x + 4x2 + -1(-25 + -15x + (5 * 3x + 3x * 3x)) = 54 + -1(2x + -7)(2x + -7)
20x + 4x2 + -1(-25 + -15x + (15x + 9x2)) = 54 + -1(2x + -7)(2x + -7)

Combine like terms: -15x + 15x = 0
20x + 4x2 + -1(-25 + 0 + 9x2) = 54 + -1(2x + -7)(2x + -7)
20x + 4x2 + -1(-25 + 9x2) = 54 + -1(2x + -7)(2x + -7)
20x + 4x2 + (-25 * -1 + 9x2 * -1) = 54 + -1(2x + -7)(2x + -7)
20x + 4x2 + (25 + -9x2) = 54 + -1(2x + -7)(2x + -7)

Reorder the terms:
25 + 20x + 4x2 + -9x2 = 54 + -1(2x + -7)(2x + -7)

Combine like terms: 4x2 + -9x2 = -5x2
25 + 20x + -5x2 = 54 + -1(2x + -7)(2x + -7)

Reorder the terms:
25 + 20x + -5x2 = 54 + -1(-7 + 2x)(2x + -7)

Reorder the terms:
25 + 20x + -5x2 = 54 + -1(-7 + 2x)(-7 + 2x)

Multiply (-7 + 2x) * (-7 + 2x)
25 + 20x + -5x2 = 54 + -1(-7(-7 + 2x) + 2x * (-7 + 2x))
25 + 20x + -5x2 = 54 + -1((-7 * -7 + 2x * -7) + 2x * (-7 + 2x))
25 + 20x + -5x2 = 54 + -1((49 + -14x) + 2x * (-7 + 2x))
25 + 20x + -5x2 = 54 + -1(49 + -14x + (-7 * 2x + 2x * 2x))
25 + 20x + -5x2 = 54 + -1(49 + -14x + (-14x + 4x2))

Combine like terms: -14x + -14x = -28x
25 + 20x + -5x2 = 54 + -1(49 + -28x + 4x2)
25 + 20x + -5x2 = 54 + (49 * -1 + -28x * -1 + 4x2 * -1)
25 + 20x + -5x2 = 54 + (-49 + 28x + -4x2)

Combine like terms: 54 + -49 = 5
25 + 20x + -5x2 = 5 + 28x + -4x2

Solving
25 + 20x + -5x2 = 5 + 28x + -4x2

Solving for variable 'x'.

Reorder the terms:
25 + -5 + 20x + -28x + -5x2 + 4x2 = 5 + 28x + -4x2 + -5 + -28x + 4x2

Combine like terms: 25 + -5 = 20
20 + 20x + -28x + -5x2 + 4x2 = 5 + 28x + -4x2 + -5 + -28x + 4x2

Combine like terms: 20x + -28x = -8x
20 + -8x + -5x2 + 4x2 = 5 + 28x + -4x2 + -5 + -28x + 4x2

Combine like terms: -5x2 + 4x2 = -1x2
20 + -8x + -1x2 = 5 + 28x + -4x2 + -5 + -28x + 4x2

Reorder the terms:
20 + -8x + -1x2 = 5 + -5 + 28x + -28x + -4x2 + 4x2

Combine like terms: 5 + -5 = 0
20 + -8x + -1x2 = 0 + 28x + -28x + -4x2 + 4x2
20 + -8x + -1x2 = 28x + -28x + -4x2 + 4x2

Combine like terms: 28x + -28x = 0
20 + -8x + -1x2 = 0 + -4x2 + 4x2
20 + -8x + -1x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
20 + -8x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(10 + x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {2, -10}